7. (5 points) The given row operations, when performed on a matrix A, result in the given matrix B. Find the determinant of A and decide if A is invertible. R1 ? R2, R2 ? R2 + 8R4, R3 ? 3R3 B = ?1 2 4 6? ?0 5 10 15? ?0 0 6 2? ?0 0 0 -1?
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Step 1: Determine the given matrix B: B = \begin{bmatrix} 1 & 2 & 4 & 6 \\ 5 & 10 & 15 & 20 \\ 6 & 2 & 8 & 6 \\ -1 & -1 & -1 & -1 \\ \end{bmatrix} Show more…
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Suppose A is a 3 X 3 matrix, and B is a 3 X 3 matrix obtained from A by performing the following elementary row operations on A : • R2 → R2 + 3R3 ; • R2 ↔ R3 . If det B = 6, find det A. -3 18 3 -6 -18
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use determinants to decide whether the given matrix is invertible. $$A=\left[\begin{array}{rrr} 2 & 0 & 3 \\ 0 & 3 & 2 \\ -2 & 0 & -4 \end{array}\right]$$
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Properties of Determinants; Cramer’s Rule
use determinants to decide whether the given matrix is invertible. $$A=\left[\begin{array}{rrr} 2 & 5 & 5 \\ -1 & -1 & 0 \\ 2 & 4 & 3 \end{array}\right]$$
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