answer problems

Learning Goal: I’m working on a algebra question and need an explanation and answer to help me learn.

1. Write the system of equations as an augmented matrix

6x−6y−4z=6
−x+y−3z=6

x−5y+4z=6

2. Write the system of equations as an augmented matrix

u − 3y = 100

n + 6y = 200

2u + n + y = 250

3.A system of equations was written as an augmented matrix where

The coefficients of the unknown variable $a$ were put in column 1
The coefficients of the unknown variable $z$ were put in column 2
The coefficients of the unknown variable $c$ were put in column 3

which was row reduced to:

1 0 0 2

0 1 0 3

0 0 1 −5

What is the solution to the original system of equations?

z=

a=

c=

4. A system of equations was written as an augmented matrix where

the coefficients of the unknown variable $r$ were put in column 1
the coefficients of the unknown variable $m$ were put in column 2
the coefficients of the unknown variable $s$ were put in column 3

which was row reduced to:

1 0 0 −4

0 1 0 4

0 0 1 −1

What is the solution to the original system of equations?

r=

m=

s=

5. Write the system of equations as an augmented matrix

$\begin{array}{}a+y=\end{array}$

$\begin{array}{}a+y+x=\end{array}$

$\begin{array}{}-a- 6y + x =200\end{array}$

$\begin{array}{}[◻ ◻ ◻◻ ]\end{array}$

$\begin{array}{}[◻ ◻ ◻◻ ]\end{array}$

$\begin{array}{}[◻ ◻ ◻◻ ]\end{array}$

$\begin{array}{}6.\; A\; system\; of\; equations\; was\; written\; as\; an\; augmented\; matrix,\; which\; was\; row\; reduced\; to:\end{array}$

$\begin{array}{}1 0 0 -1\end{array}$

$\begin{array}{}0 1 0 -6\end{array}$

$\begin{array}{}0 0 1 -2\end{array}$

$\begin{array}{}What\; is\; the\; solution\; to\; the\; original\; system\; of\; equations?\end{array}$

$\begin{array}{}y=\end{array}$

$\begin{array}{}x=\end{array}$

$\begin{array}{}z=\end{array}$

$\begin{array}{}7.\; Write\; the\; augmented\; matrix\; of\; the\; system\; and\; use\; it\; to\; solve\; the\; system.\; If\; the\; system\; has\; an\; infinite\; number\; of\; solutions,\; express\; them\; in\; terms\; of\; the\; parameter z.\end{array}$

$\begin{array}{c}\mathrm{\{15}x+5y+z=-75\end{array}$

$\begin{array}{c}18x+5y+3z=-94\end{array}$

$\begin{array}{c}6x+2y+z=-33\end{array}$

$\begin{array}{c}\mathrm{x=}\end{array}$

$\begin{array}{c}\mathrm{y=}\end{array}$

$\begin{array}{c}\mathrm{z=}\end{array}$

$\begin{array}{c}\mathrm{8.\; Write\; the\; augmented\; matrix\; of\; the\; system\; and\; use\; it\; to\; solve\; the\; system.\; If\; the\; system\; has\; an\; infinite\; number\; of\; solutions,\; express\; them\; in\; terms\; of\; the\; parameter z.}\end{array}$

$\begin{array}{c}8x+3y+15z=-38\end{array}$

$\begin{array}{c}12x+6y+18z=-60\end{array}$

$\begin{array}{c}4x+3y+\; 3z=-22\end{array}$

$\begin{array}{c}\mathrm{x=}\end{array}$

$\begin{array}{c}\mathrm{y=}\end{array}$

$\begin{array}{c}\mathrm{z=}\end{array}$

$\begin{array}{c}\mathrm{9.\; Write\; the\; augmented\; matrix\; as\; a\; system\; of\; equations}\end{array}$

[0 2 1 250

$\begin{array}{c}\mathrm{0 1 0 400}\end{array}$

$\begin{array}{c}\mathrm{-1 -3 1 100]}\end{array}$

$\begin{array}{c}\mathrm{\_\_\_\; x+\; \_\_\_y+\; \_\_\_z=\; \_\_\_}\end{array}$

$\begin{array}{c}\mathrm{\_\_\_x+\; \_\_\_y+\; \_\_\_z=\; \_\_\_}\end{array}$

$\begin{array}{c}\mathrm{\_\_\_x+\; \_\_\_y+\; \_\_\_\; z=\; \_\_\_}\end{array}$

10. Let

$M=\; [\; 1\; 4\; -2$

5 -3 3]

[____ ____ ____

____ ____ ____]

11. Given $A=\; [2\; -1\; -7\; Given A= [250$

$-1\; 1\; 6\; 400$

-1 -1 -5] 150]

Solve the matrix equation $Ax=b$ for $x$

$x=\; =$

$[\; \_\_\_$

$\_\_\_$

$\_\_\_]$

$12.\; Write\; out\; the\; matrix\; equation\; for\; this\; given\; system\; of\; equations$

$z+2x=200$

−3z + y − 5x = 300

3z + 7x = 150