Question

Solve the following system using a matrix. 7a - b = -1 -4a - 2b = -2

Answer 1

Answer:

a = 0, b = 1

Step-by-step explanation:

Given system equation is,

7a - b = -1

-4a - 2b = -2

Since, the matrix form of this system of equation is,

$\begin{bmatrix} 7& -1\\ -4 & -2\end{bmatrix}\begin{bmatrix}a\\b\end{bmatrix}=\begin{bmatrix}-1\\ -2\end{bmatrix}$

Let,

$A=\begin{bmatrix} 7& -1\\ -4 & -2\end{bmatrix}$

$X=\begin{bmatrix}a\\ b\end{bmatrix}$

$B=\begin{bmatrix}-1\\ -2\end{bmatrix}$

$\because AX = B\implies X = A^{-1}B$

$adj(A) = \begin{bmatrix} -2& 1\\4& 7\end{bmatrix}$

Also,

|A| = -18

$\implies A^{-1}=-\frac{1}{18}\begin{bmatrix} -2& 1\\4& 7\end{bmatrix}$

$\implies X = -\frac{1}{18}\begin{bmatrix} -2& 1\\4& 7\end{bmatrix}.\begin{bmatrix}-1\\ -2\end{bmatrix}$

$X=-\frac{1}{18}\begin{bmatrix}2-2\\ -4-14\end{bmatrix}$

$X=-\frac{1}{18}\begin{bmatrix}0\\ -18\end{bmatrix}$

$X=\begin{bmatrix}0\\ 1\end{bmatrix}$

$\implies \begin{bmatrix}a\\ b\end{bmatrix}=\begin{bmatrix}0\\ 1\end{bmatrix}$

By comparing,

a = 0, b = 1

Answer 2

1. a=-1+b/7 is the right answer.    First you had to add by b from both sides of equation, and it gave us, $7a-b+b=-1+b$. And then simplify, and it gave us, $7a=-1+b$. Divide by 7 from both sides of equation, and it gave us, $\frac{7a}{7}=-\frac{1}{7}+ \frac{b}{7}$. Finally simplify, and it gave us the answer is a=-1+b/7 is the right answer.

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2. a=-b-1/2 is the right answer.     First you had to add by 2b from both sides of equation, and it gave us, $-4a-2b+2b=-2+2b$. And then simplify, and it gave us, $-4a=-2+2b$. Next you can also divide by -4 from both sides of equation, and it gave us, $\frac{-4a}{-4}=-\frac{2}{-4}+\frac{2b}{-4}$. Finally simplify, and it gave us the answer is a=-b-1/2 is the right answer. Hope this helps! And thank you for posting your question at here on brainly, and have a great day. -Charlie

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