Solve this linear system using matrices: x1 + 2x2 − x3 = −4 x1 + 2x2 + x3 = 2 −x1 − x2 + 2x3 = 6

In matrix form, the system is

Solving this "using matrices" is a bit ambiguous but brings to mind two standard methods.

Compute the inverse of the coefficient matrix using the formula

where is the coefficient matrix, is its determinant, is the cofactor matrix, and denotes the matrix transpose.

We compute the determinant by a Laplace expansion along the first column:

The cofactor matrix is

which makes the inverse

Finally,

Take the augmented matrix

Subtract row 1 from row 2, and -(row 1) from row 3:

Multiply row 2 by 1/2:

The second row tells us that

Then in the third row,

Then in the first row,

555.99.

step-by-step explanation:

hope this

i think the correct option is the second option.