Question

Find the determinant of the coefficient matrix
3x+4y=0
-2x+3y=-17

Answer 1

17

Explanation:

You want the determinant of the coefficient matrix for the equations ...

• 3x +4y = 0
• -2x +3y = -17

Coefficient matrix

The matrix of coefficients is formed by listing the coefficients of the equation variables on rows of the matrix, in the same order for each row.

Here it is:

`\left[\begin{array}{cc}3&4\\-2&3\end{array}\right]`

Determinant

The determinant of a 2×2 matrix is the difference between the product of terms on the down diagonal and that on the up diagonal.

det = (3)(3) -(-2)(4) = 9 + 8 = 17

The determinant of the coefficient matrix is 17.

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Additional comment

Many scientific and graphing calculators can find this for you. A spreadsheet can be useful for this purpose, too.

The determinant is only defined for a square matrix. For sizes larger than 2×2, the arithmetic is a little different.