Provide an appropriate response.
-Indicate whether the following statement is If every element of a $14 \times 14$ matrix is multiplied by -3,
the determinant of the new matrix is -3 times the determinant of the original matrix.

Question

Quizplus · Accepted Answer

When every element of a square matrix is multiplied by a scalar (in this case, -3), the determinant of the new matrix is the scalar raised to the power of the size of the matrix (here, 14) times the determinant of the original matrix. Therefore, the determinant of the new matrix is $(-3)^{14}$ times the determinant of the original matrix, not -3 times.

Provide an Appropriate Response 14×1414 \times 1414×14 Matrix Is Multiplied by -3, the Determinant of the New

Provide an Appropriate Response $14 \times 14$ Matrix Is Multiplied by -3,
the Determinant of the New