Use the theorem for three linearly independent vectors (that is, calculate a determinant) to determine whether the given vectors u, v, and w are linearly dependent or independent. u = [ 3, -1, 6], v = [ 6, 2, -7], w = [ 9, 1, -1] The determinant of the matrix formed by u, v, and w is [ ]. (Simplify your answer.)

          Use the theorem for three linearly independent vectors (that is, calculate a determinant) to determine whether the given vectors u, v, and w are linearly dependent or independent.

u = [ 3, -1, 6], v = [ 6, 2, -7], w = [ 9, 1, -1]

The determinant of the matrix formed by u, v, and w is [ ].
(Simplify your answer.)

Use the theorem for three linearly independent vectors (that is, calculate a determinant) to determine whether the given vectors u, v, and w are linearly dependent or independent.

u = [ 3, -1, 6], v = [ 6, 2, -7], w = [ 9, 1, -1]

The determinant of the matrix formed by u, v, and w is [ ].
(Simplify your answer.)

Added by Sandra G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/02/2023

Step 1

First, let's write the given vectors U, V, and W as column vectors: U = \begin{bmatrix} u_1 \\ u_2 \\ u_3 \end{bmatrix}, V = \begin{bmatrix} v_1 \\ v_2 \\ v_3 \end{bmatrix}, W = \begin{bmatrix} w_1 \\ w_2 \\ w_3 \end{bmatrix} Now, let's form a matrix A using Show more…

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Use the theorem for three linearly independent vectors (that is, calculate a determinant) to determine whether the given vectors u, v, and w are linearly dependent or independent. The determinant of the matrix formed by u, v, and w is (Simplify your answer.)