WeBWorK Standalone Renderer

Consider the matrix

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$	-4	2	-7	$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$
	-16	13	1
	12	-2	-2
	-8	6	5

(a) On the matrix above, perform the row operation $\frac{1}{-4} R_1 \to R_1$ . The new matrix is:

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$				$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

(b) Using the matrix obtained in your answer for part (a) as the initial matrix, next perform the row operations

$\qquad \qquad + 16 R_1 +R_2 \to R_2$

$\qquad \qquad -12 R_1 + R_3 \to R_3.$

$\qquad \qquad + 8 R_1 + R_4 \to R_4.$

The new matrix is:

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$				$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

(c) Using the matrix obtained in your answer for part (b) as the initial matrix, next perform the row operations

$\qquad \qquad \frac{1}{5} R_2 \to R_2$

$\qquad \qquad \frac{1}{4} R_3 \to R_3.$

$\qquad \qquad \frac{1}{2} R_4 \to R_4.$

The new matrix is:

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$				$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

You can earn partial credit on this problem.