7. Systems of Equations & Matrices

Determinants and Cramer's Rule

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.
$[\begin{matrix} x & y & z \end{matrix}] = [\begin{matrix} 21 & 6 \end{matrix}]$
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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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Textbook Question
Given $A = [\begin{matrix} 4 & - 2 \\ 3 & 1 \end{matrix}],$ and $C = \left[ \begin{matrix} -5 & 4 & 1 \\ 0 & 3 & 6 \end{matrix} \right]$ , find each product, if possible. See Examples 5–7. BA
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Textbook Question
Given $A = [\begin{matrix} 4 & - 2 \\ 3 & 1 \end{matrix}],$ , and $C = \left[ \begin{matrix} -5 & 4 & 1 \\ 0 & 3 & 6 \end{matrix} \right]$ , find each product, if possible. See Examples 5–7. BC
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Textbook Question
Given $A = [\begin{matrix} 4 & - 2 \\ 3 & 1 \end{matrix}],$ , and $C = \left[ \begin{matrix} -5 & 4 & 1 \\ 0 & 3 & 6 \end{matrix} \right]$ , find each product, if possible. See Examples 5–7. AB
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Textbook Question
For each pair of matrices A and B, find (a) AB and (b) BA. See Example 7. $A = [\begin{matrix} 3 & 4 \\ - 2 & 1 \end{matrix}],$
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Textbook Question
For each pair of matrices A and B, find (a) AB and (b) BA. $A = [\begin{matrix} 0 & - 5 \\ - 4 & 2 \end{matrix}],$
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Textbook Question
For each pair of matrices A and B, find (a) AB and (b) BA. $A = [\begin{matrix} 0 & 1 & - 1 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}],$
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Textbook Question
Find AB and BA for the following matrices.
$A = [\begin{matrix} a & b \\ c & d \end{matrix}]$
Matrix B acts as the multiplicative element for 2 $\times$ 2 square matrices.
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Textbook Question
Find the values of the variables for which each statement is true, if possible.
$[\begin{matrix} 5 & x + 2 \\ - 6 y & z \end{matrix}] = [\begin{matrix} a & 3 x - 1 \\ 5 y & 9 \end{matrix}]$
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