7. Systems of Equations & Matrices

Determinants and Cramer's Rule

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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Textbook Question
Find the values of the variables for which each statement is true, if possible.
$[\begin{matrix} - 7 + z & 4 r & 8 s \\ 6 p & 2 & 5 \end{matrix}] + [\begin{matrix} - 9 & 8 r & 3 \\ 2 & 5 & 4 \end{matrix}] = [\begin{matrix} 2 & 36 & 27 \\ 20 & 7 & 12 a \end{matrix}]$
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Textbook Question
Find the values of the variables for which each statement is true, if possible.
$[\begin{matrix} 0 & 5 & x \\ - 1 & 3 & y + 2 \\ 4 & 1 & z \end{matrix}] = [\begin{matrix} 0 & w & 6 \\ - 1 & 3 & 0 \\ 4 & 1 & 8 \end{matrix}]$
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Textbook Question
Find the values of the variables for which each statement is true, if possible.
$[\begin{matrix} x & y & z \end{matrix}] = [\begin{matrix} 21 & 6 \end{matrix}]$
50
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Textbook Question
Find the values of the variables for which each statement is true, if possible.
$[\begin{matrix} x + 2 & y - 6 \\ z - 3 & w + 5 \end{matrix}] = [\begin{matrix} - 2 & 8 \\ 0 & 3 \end{matrix}]$
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Textbook Question
Find the values of the variables for which each statement is true, if possible.
$[\begin{matrix} - 3 & a \\ b & 5 \end{matrix}] = [\begin{matrix} c & 0 \\ 4 & d \end{matrix}]$
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Textbook Question
Find the dimension of each matrix. Identify any square, column, or row matrices. See the discussion preceding Example 1.
$∣ \begin{matrix} - 9 \end{matrix} ∣$
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Textbook Question
Find each product, if possible.
$[\begin{matrix} - 2 & - 3 & - 4 \\ 2 & - 1 & 0 \\ 4 & - 2 & 3 \end{matrix}] [\begin{matrix} 0 & 1 & 4 \\ 1 & 2 & - 1 \\ 3 & 2 & - 2 \end{matrix}]$
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