Question

Find the determinant of the coefficient matrix of the linear system?

Answer 1

A coefficient matrix is a matrix consisting of the coefficients of the variables in a set of linear equations. In this case, the coefficient matrix is:

$A=\begin{bmatrix}{3} & {-2} \\ {2} & {5}\end{bmatrix}$

The determinant of a 2x2 matrix:

$\begin{bmatrix}a & {b} \\ c & {d}\end{bmatrix}$

is ad - cb. Applying this formula to matrix A, we get:

$\det (A)=3\cdot5-2\cdot(-2)=15+4=19$

Given that the determinant is not zero, then the system of equations has exactly one solution