Question

I NEED HELP PLEASE, THANKS! Use Cramer's Rule to find the solution of the system of linear equations, if a unique solution exists. –5x + 2y – 2z = 26 3x + 5y + z = –22 –3x – 5y – 2z = 21 A. (–1, –7, 2) B. (–6, –1, 1) C. (–1, 3, 1) D. no unique solution

Answer 1

-5 x + 2 y - 2 z = 263 x + 5 y + z = -22 - 3 x - 5 y - 2 z = 21

Answer is x=-6,\:z=1,\:y=-1

Answer 2

Option B

Explanation:

We are given the following system of equations -

`\begin{bmatrix}-5x+2y-2z=26\\ 3x+5y+z=-22\\ -3x-5y-2z=21\end{bmatrix}`

Now by Cramer's Rule, we would first write down the matrix of the coefficients , replacing each column with the answer column -

`\begin{bmatrix}-5&2&-2\\ 3&5&1\\ -3&-5&-2\end{bmatrix}` ,

`\begin{bmatrix}26\\ -22\\ 21\end{bmatrix}`

Replace each column of the coefficients shown at the top, with the answer column at the bottom respectively -

`\begin{bmatrix}-5&2&26\\ 3&5&-22\\ -3&-5&21\end{bmatrix}`

Now solve through Cramer's Rule -

x = Dx / D = - 6,

y = Dy / D = - 1,

z = Dz / D = 1

Solution = ( - 6, - 1, 1 ) = Option B