Question

If A =( 8 −4 1 10 0 6 8 1 6 ), find A-1. Hence solve the following system of equations: 8x – 4y + z = 5; 10x + 6z =4; 8x + y +6z = 5 2 .​

Answer 1

Answer:

2y is the answer m not sure

Answer 2

Step-by-step-Explanation:

Given:

$A=\left[\begin{array}{ccc}8&-4&1\\10&0&6\\8&1&6\end{array}\right]$

*To find: Find A inverse and hence solve the following system of equations: 8x – 4y + z = 5; 10x + 6z =4; 8x + y +6z = 5 .

Solution:

Step 1: Find determinant of A

$|A|=\left|\begin{array}{ccc}8&-4&1\\10&0&6\\8&1&6\end{array}\right|\\\\|A|=8(0-6)+4(60-48)+1(10-0)\\\\|A|=-48+48+10\\\\|A|=10$

Step 2: Find co-factor matrix

$C=\left[\begin{array}{ccc}-6&-12&10\\25&40&-40\\-24&-38&40\end{array}\right]$

Step 3: Find Adj ,by transponse of co-factor matrix

$C=\left[\begin{array}{ccc}-6&25&-24\\-12&40&-38\\10&-40&40\end{array}\right]$

Step 4: Write A inverse

$A^{-1}=\frac{1}{10}\left[\begin{array}{ccc}-6&25&-24\\-12&40&-38\\10&-40&40\end{array}\right]$

Step 5: Write equations in matrix form

AX=B

$\left[\begin{array}{ccc}8&-4&1\\10&0&6\\8&1&6\end{array}\right]\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}5\\4\\5\end{array}\right]$

Step 6: Solution is

$X=A^{-1}B\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\frac{1}{10}\left[\begin{array}{ccc}-6&25&-24\\-12&40&-38\\10&-40&40\end{array}\right]\left[\begin{array}{ccc}5\\4\\5\end{array}\right]$

$\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\frac{1}{10}\left[\begin{array}{ccc}-30+100-120\\-60+160-190\\50-160+200\end{array}\right]$

$\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\frac{1}{10}\left[\begin{array}{ccc}-50\\-90\\90\end{array}\right]$

$\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}-5\\-9\\9\end{array}\right]$

Final answer:

$x=-5\\y=-9\\z=9$

Hope it helps you.

*Note: Corrected.

To learn more on brainly:

Solve these three equations using matrix inversion method:

5x-6y-7z=7

6x-4y+10z=-34

2x+4y-3z=29

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