Question

What is the determinant of the coefficient matrix of the system
4x-6y+0z=-7
3x+3y+0z = -2
2x– 12y+0z=-1

Answer 1

All of the z coefficients are zero. This means that the matrix will have a column full of zeroes:

$\left(\begin{array}{ccc}4&-6&0\\3&3&0\\2&-12&0\end{array}\right)$

And every time a matrix has a row/column full of zeroes, its determinant is zero.

Answer 2

All of the z coefficients are zero. This means that the matrix will have a column full of zeroes:

And every time a matrix has a row/column full of zeroes, its determinant is zero.

In linear algebra, a coefficient matrix is a matrix consisting of the coefficients of the variables in a set of linear equations. The matrix is used in solving systems of linear equations.

What are a coefficient matrix and an augmented matrix?

Solution: A coefficient matrix is a matrix made up of the coefficients from a system of linear equations. An augmented matrix is similar in that it, too, is a coefficient matrix, but in addition, it is augmented with a column consisting of the values on the right-hand side of the equations of the linear system.

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