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Multiplying matrices (pre-defined sizes in answers)

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An $n \\times p$ matrix $A$ can be multiplied by a $p \\times n$ matrix $B$ to form an $n \\times m$ matrix $AB=C$.

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The number of columns of $A$ must match the number of rows of $B$.

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The element in the $i^{th}$ row and $j^{th}$ column of $C$ is obtained by multiplying the $i^{th}$ row of $A$ with the $j^{th}$ column of $B$.

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We are asked to carry out matix multiplications.

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First of all, you should always check that the multiplication is even possible. Write down the dimensions (in order) of the two matrices:

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The number of columns in the first must match the number of rows in the second. As a bonus this will also give you the dimensions of the product matrix.

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The multiplication is then carried out moving across the rows of the first matrix and down the columns of the second:

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Using this techniques will give:

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$A_1A_2=\\var{A1}\\var{A2}$

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$A_1 A_2=\\var{prodA}$ 

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$B_1B_2=\\var{B1}\\var{B2}$

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$B_1 B_2=\\var{prodB}$ 

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$C_1C_2=\\var{C1}\\var{C2}$

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$C_1 C_2=\\var{prodC}$

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Carry out the following multiplications:

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$A_1A_2=\\var{A1}\\var{A2}$

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$A_1 A_2=$ [[0]]

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$B_1B_2=\\var{B1}\\var{B2}$

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$B_1 B_2=$ [[1]]

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$C_1C_2=\\var{C1}\\var{C2}$

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$C_1 C_2=$ [[2]]

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