Properties of Determinants: Row Operations, Products, Transposes Worksheet with Answer Key

What's on the worksheet

1. The 4 × 4 matrix A has rows r_1, r_2, r_3, r_4, in that order, and A = -5.
2. Find each determinant by using the properties of determinants, with at most one line of arithmetic.
3. Find A by reducing A to triangular form, where A = \begin{bmatrix} 1 & -2 & 1 & 3 \\ 2 & -4 & 5 & 9 \\ -2 & 7 & 1 & -9 \\ 3 & -6 & 0 & 4 \end{bmatrix}
4. A and B are 4 × 4 matrices with A = -2 and B = -4.
7. For a real number x, let M = \begin{bmatrix} x & 2 & 2 & 2 \\ 2 & x & 2 & 2 \\ 2 & 2 & x & 2 \\ 2 & 2 & 2 & x \end{bmatrix} Use row operations to…