7. Systems of Equations & Matrices

Determinants and Cramer's Rule

Textbook Question
Fill in the blank(s) to correctly complete each sentence. For the following statement to be true, the value of x must be ____, and the value of y must be ____.
$[\begin{matrix} 3 & - 6 \\ 5 & 1 \end{matrix}] = [\begin{matrix} x + 1 & - 6 \\ 5 & y + 1 \end{matrix}]$
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Textbook Question
If the dimension of matrix A is 3 $\times$ 2 and the dimension of matrix B is 2 $\times$ 6, then the dimension of AB is ____.
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Textbook Question
Find each product, if possible.
$[\begin{matrix} \sqrt{3} & 1 \\ 2 \sqrt{5} & 3 \sqrt{2} \end{matrix}] [\begin{matrix} \sqrt{3} & - \sqrt{6} \\ 4 \sqrt{3} & 0 \end{matrix}]$
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Textbook Question
Find each product, if possible.
$[\begin{matrix} \sqrt{2} & \sqrt{2} & - \sqrt{18} \\ \sqrt{3} & \sqrt{27} & 0 \end{matrix}] [\begin{matrix} 8 & - 10 \\ 9 & 12 \\ 0 & 2 \end{matrix}]$
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Textbook Question
Find each product, if possible.
$[\begin{matrix} 3 & - 4 & 1 \\ 5 & 0 & 2 \end{matrix}] [\begin{matrix} - 1 \\ 4 \\ 2 \end{matrix}]$
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Textbook Question
Find each product, if possible.
$[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} - 1 \\ 7 \end{matrix}]$
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Textbook Question
Let $A = [\begin{matrix} - 2 & 4 \\ 0 & 3 \end{matrix}]$ and $B = \left[ \begin{matrix} -6 & 2 \\ 4 & 0 \end{matrix} \right]$ . Find each of the following.
-A + (1/2)B
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Textbook Question
Let and . Find each of the following. See Examples 2 –4.
2A + 4B
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Textbook Question
Let and . Find each of the following. See Examples 2 –4.
(3/2)B
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Textbook Question
Find each sum or difference, if possible. See Examples 2 and 3.
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Textbook Question
Find each sum or difference, if possible.
$[\begin{matrix} \sqrt{3} & - 4 \\ 2 & - \sqrt{5} \\ - 8 & \sqrt{8} \end{matrix}] - [\begin{matrix} 2 \sqrt{3} & 9 \\ - 2 & \sqrt{5} \\ - 7 & 3 \sqrt{2} \end{matrix}]$
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Textbook Question
Find each sum or difference, if possible.
$[\begin{matrix} - 4 & 3 \end{matrix}] - [\begin{matrix} 5 & 8 & 2 \end{matrix}]$
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Textbook Question
Find each sum or difference, if possible. See Examples 2 and 3.
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Textbook Question
Find each sum or difference, if possible.
$[\begin{matrix} 2 & 4 & 6 \end{matrix}] + [\begin{matrix} - 2 \\ - 4 \\ - 6 \end{matrix}]$
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Textbook Question
Find each sum or difference, if possible.
$[\begin{matrix} 6 & - 9 & 2 \\ 4 & 1 & 3 \end{matrix}] + [\begin{matrix} - 8 & 2 & 5 \\ 6 & - 3 & 4 \end{matrix}]$
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