7. Systems of Equations & Matrices

Determinants and Cramer's Rule

Textbook Question
Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I_n.)
$[\begin{matrix} 5 & 7 \\ 2 & 3 \end{matrix}]$
477
views
Textbook Question
Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I_n.)
$[\begin{matrix} 0 & 1 & 0 \\ 0 & 0 & - 2 \\ 1 & - 1 & 0 \end{matrix}]$
465
views
Textbook Question
Find the inverse, if it exists, for each matrix. $[\begin{matrix} - 1 & 2 \\ - 2 & - 1 \end{matrix}]$
432
views
Textbook Question
Find the inverse, if it exists, for each matrix. $[\begin{matrix} - 1 & - 2 \\ 3 & 4 \end{matrix}]$
481
views
Textbook Question
Find the inverse, if it exists, for each matrix. $[\begin{matrix} 5 & 10 \\ - 3 & - 6 \end{matrix}]$
430
views
Textbook Question
Find the inverse, if it exists, for each matrix. $[\begin{matrix} 1 & 0 & 1 \\ 0 & - 1 & 0 \\ 2 & 1 & 1 \end{matrix}]$
436
views
Textbook Question
Find the inverse, if it exists, for each matrix. $[\begin{matrix} 2 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4 \end{matrix}]$
432
views
Textbook Question
Find the inverse, if it exists, for each matrix. $[\begin{matrix} 2 & 2 & - 4 \\ 2 & 6 & 0 \\ - 3 & - 3 & 5 \end{matrix}]$
457
views
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 ____.
$[\begin{matrix} 3 & - 6 \\ 5 & 1 \end{matrix}] = [\begin{matrix} x + 1 & - 6 \\ 5 & y + 1 \end{matrix}]$
38
views
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 ____.
67
views
Textbook Question
Find each product, if possible.
$[\begin{matrix} \sqrt{3} & 1 \\ 2 \sqrt{5} & 3 \sqrt{2} \end{matrix}] [\begin{matrix} \sqrt{3} & - \sqrt{6} \\ 4 \sqrt{3} & 0 \end{matrix}]$
44
views
Textbook Question
Find each product, if possible.
$[\begin{matrix} \sqrt{2} & \sqrt{2} & - \sqrt{18} \\ \sqrt{3} & \sqrt{27} & 0 \end{matrix}] [\begin{matrix} 8 & - 10 \\ 9 & 12 \\ 0 & 2 \end{matrix}]$
62
views
Textbook Question
Find each product, if possible.
$[\begin{matrix} 3 & - 4 & 1 \\ 5 & 0 & 2 \end{matrix}] [\begin{matrix} - 1 \\ 4 \\ 2 \end{matrix}]$
42
views
Textbook Question
Find each product, if possible.
$[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}] [\begin{matrix} - 1 \\ 7 \end{matrix}]$
63
views
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
43
views