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Add qs on dot product in matrix form
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‎03-matrices/questions/2-4-dot-product.json‎

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[
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{
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"question": "Let $\\mathbf{u} = \\begin{bmatrix}3 & -2\\end{bmatrix}^T$ and $\\mathbf{v} = \\begin{bmatrix}4 & 1\\end{bmatrix}^T$. Find $\\mathbf{u}^T \\mathbf{v}$.",
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"type": "numeric",
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"answers": [
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{
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"type": "value",
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"value": 10,
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"correct": true,
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"feedback": "Correct!"
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},
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{
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"type": "default",
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"feedback": "Incorrect. Recall that is the sum of the componentwise products."
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}
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]
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},
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{
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"question": "Let $\\mathbf{u} = \\begin{bmatrix}-1 & 0 & 5\\end{bmatrix}^T$ and $\\mathbf{v} = \\begin{bmatrix}3 & 2 & -2\\end{bmatrix}^T$. Find $\\mathbf{u}^T \\mathbf{v}$.",
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"type": "numeric",
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"answers": [
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{
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"type": "value",
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"value": -13,
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"correct": true,
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"feedback": "Correct!"
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},
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{
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"type": "default",
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"feedback": "Incorrect. Recall that is the sum of the componentwise products."
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}
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]
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},
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{
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"question": "Let $\\mathbf{u} = \\begin{bmatrix}2 & 2\\end{bmatrix}^T$ and $\\mathbf{v} = \\begin{bmatrix}3 & -4\\end{bmatrix}^T$. Find $\\mathbf{u}^T \\mathbf{v}$.",
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"type": "numeric",
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"answers": [
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{
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"type": "value",
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"value": -2,
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"correct": true,
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"feedback": "Correct!"
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},
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{
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"type": "default",
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"feedback": "Incorrect. Recall that is the sum of the componentwise products."
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}
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]
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},
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{
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"question": "Let $\\mathbf{u} = \\begin{bmatrix}0 & -3 & 1\\end{bmatrix}^T$ and $\\mathbf{v} = \\begin{bmatrix}5 & 2 & 0\\end{bmatrix}^T$. Find $\\mathbf{u}^T \\mathbf{v}$.",
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"type": "numeric",
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"answers": [
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{
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"type": "value",
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"value": -6,
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"correct": true,
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"feedback": "Correct!"
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},
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{
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"type": "default",
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"feedback": "Incorrect. Recall that is the sum of the componentwise products."
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}
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]
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},
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{
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"question": "Let $\\mathbf{u} = \\begin{bmatrix}-2 & -2 & -2\\end{bmatrix}^T$ and $\\mathbf{v} = \\begin{bmatrix}-1 & 0 & 3\\end{bmatrix}^T$. Find $\\mathbf{u}^T \\mathbf{v}$.",
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"type": "numeric",
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"answers": [
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{
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"type": "value",
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"value": -4,
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"correct": true,
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"feedback": "Correct!"
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},
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{
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"type": "default",
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"feedback": "Incorrect. Recall that is the sum of the componentwise products."
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}
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]
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},
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{
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"question": "Let $\\mathbf{u} = \\begin{bmatrix}4 & -5\\end{bmatrix}^T$ and $\\mathbf{v} = \\begin{bmatrix}0 & 1\\end{bmatrix}^T$. Find $\\mathbf{u}^T \\mathbf{v}$.",
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"type": "numeric",
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"answers": [
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{
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"type": "value",
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"value": -5,
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"correct": true,
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"feedback": "Correct!"
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},
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{
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"type": "default",
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"feedback": "Incorrect. Recall that is the sum of the componentwise products."
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}
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]
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},
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{
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"question": "Let $\\mathbf{u} = \\begin{bmatrix}1 & 1 & 1\\end{bmatrix}^T$ and $\\mathbf{v} = \\begin{bmatrix}5 & 4 & 3\\end{bmatrix}^T$. Find $\\mathbf{u}^T \\mathbf{v}$.",
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"type": "numeric",
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"answers": [
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{
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"type": "value",
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"value": 12,
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"correct": true,
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"feedback": "Correct!"
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},
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{
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"type": "default",
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"feedback": "Incorrect. Recall that is the sum of the componentwise products."
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}
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]
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},
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{
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"question": "Let $\\mathbf{u} = \\begin{bmatrix}-3 & -4\\end{bmatrix}^T$ and $\\mathbf{v} = \\begin{bmatrix}-2 & 1\\end{bmatrix}^T$. Find $\\mathbf{u}^T \\mathbf{v}$.",
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"type": "numeric",
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"answers": [
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{
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"type": "value",
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"value": 2,
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"correct": true,
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"feedback": "Correct!"
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},
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{
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"type": "default",
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"feedback": "Incorrect. Recall that is the sum of the componentwise products."
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}
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]
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},
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{
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"question": "Let $\\mathbf{u} = \\begin{bmatrix}2 & 0 & -1\\end{bmatrix}^T$ and $\\mathbf{v} = \\begin{bmatrix}3 & -5 & 2\\end{bmatrix}^T$. Find $\\mathbf{u}^T \\mathbf{v}$.",
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"type": "numeric",
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"answers": [
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{
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"type": "value",
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"value": 4,
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"correct": true,
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"feedback": "Correct!"
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},
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{
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"type": "default",
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"feedback": "Incorrect. Recall that is the sum of the componentwise products."
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}
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]
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},
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{
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"question": "Let $\\mathbf{u} = \\begin{bmatrix}5 & 0 & 0\\end{bmatrix}^T$ and $\\mathbf{v} = \\begin{bmatrix}0 & 5 & 0\\end{bmatrix}^T$. Find $\\mathbf{u}^T \\mathbf{v}$.",
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"type": "numeric",
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"answers": [
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{
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"type": "value",
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"value": 0,
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"correct": true,
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"feedback": "Correct!"
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},
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{
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"type": "default",
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"feedback": "Incorrect. Recall that is the sum of the componentwise products."
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}
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]
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}
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]

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