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Multiplication of matrices.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

The matrices $A$, $B$, $C$ and $D$ are defined as:

\n

\\[A=\\var{A}\\qquad B=\\var{B}\\qquad C=\\var{C}\\qquad D=\\var{D}\\]

\n

Multiply the matrices, as stated below. You should adjust the number of rows and columns to obtain the correct shape of the answer matrix.

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Calculate $AB$.

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Calculate $CB$.

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Calculate $BD$.

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Calculate $DC$.

", "correctAnswer": "D*C", "correctAnswerFractions": false, "numRows": "1", "numColumns": "1", "allowResize": true, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": "5", "minRows": 1, "maxRows": "5"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Matrix multiplication shape", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "tags": [], "metadata": {"description": "

Multiplication of matrices.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

The matrices $A$, $B$, $C$ and $D$ are defined as:

\n

\\[A=\\var{A}\\qquad B=\\var{B}\\qquad C=\\var{C}\\qquad D=\\var{D}\\]

\n

Describe the shape of the answer matrix.

\n

(Recall that an $m\\times n$ matrix has $m$ rows and $n$ columns.)

", "advice": "

When you multiply two matrices $A$ and $B$, the answer $AB$ has the same number of rows as $A$ and the same number of columns as $B$.

\n

So if $A$ is an $m\\times n$ matrix and $B$ is an $n\\times p$ matrix, then $AB$ is an $m\\times p$ matrix.

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\n

$AB:\\qquad$ [[0]]$\\times\\;$ [[1]]

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$CB:\\qquad$ [[0]]$\\times\\;$ [[1]]

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$BD:\\qquad$ [[0]]$\\times\\;$ [[1]]

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$DC:\\qquad$ [[0]]$\\times\\;$ [[1]]

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Multiplication of matrices.

", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "

The matrices $A$, $B$, $C$ and $D$ are defined as:

\n

\\[A=\\var{A}\\qquad B=\\var{B}\\qquad C=\\var{C}\\qquad D=\\var{D}\\]

\n

Which of the following matrix products can be calculated?

", "advice": "

For two matrices $A$ and $B$, it is possible to calculate $AB$ if the number of columns in matrix $A$ is the same as the number of rows in matrix $B$. Otherwise it is not possible to multiply them.

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$AB$

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$AC$

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$BC$

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$CB$

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$AD$

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$BD$

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$DC$

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$DB$

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