WeBWorK Standalone Renderer

Consider the matrix

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$	-4	2	-7	6	$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$
	-16	11	-6	5
	4	1	-2	5
	-16	11	-6	1

(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

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

$\qquad \qquad -4 R_1 + R_3 \to R_3.$

$\qquad \qquad + 16 R_1 + R_4 \to R_4.$

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

$\qquad \qquad \frac{1}{3} R_2 \to R_2$

$\qquad \qquad \frac{1}{3} R_3 \to R_3.$

$\qquad \qquad \frac{1}{3} R_4 \to R_4.$

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.