Question

Determine whether or not the following sets are linearly independent in the given vectors spaces. a) {egin{bmatrix} 1 \ -1 \ 2 end{bmatrix}, egin{bmatrix} 1 \ -2 \ 1 end{bmatrix}, egin{bmatrix} 1 \ 1 \ 4 end{bmatrix}} in mathbb{R}^3 b) {egin{bmatrix} 1 \ -1 \ 2 end{bmatrix}, egin{bmatrix} 2 \ 0 \ 1 end{bmatrix}, egin{bmatrix} -1 \ 2 \ -1 end{bmatrix}} in mathbb{R}^3 c) {x^3 + 2x^2, -x^2 + 3x + 1, x^3 - x^2 + 2x - 1} in P_3(mathbb{R})

          Determine whether or not the following sets are linearly independent in the
given vectors spaces.
a) {egin{bmatrix} 1 \ -1 \ 2 end{bmatrix}, egin{bmatrix} 1 \ -2 \ 1 end{bmatrix}, egin{bmatrix} 1 \ 1 \ 4 end{bmatrix}} in mathbb{R}^3
b) {egin{bmatrix} 1 \ -1 \ 2 end{bmatrix}, egin{bmatrix} 2 \ 0 \ 1 end{bmatrix}, egin{bmatrix} -1 \ 2 \ -1 end{bmatrix}} in mathbb{R}^3
c) {x^3 + 2x^2, -x^2 + 3x + 1, x^3 - x^2 + 2x - 1} in P_3(mathbb{R})

Determine whether or not the following sets are linearly independent in the
given vectors spaces.
a) eginbmatrix 1 -1 2 endbmatrix, eginbmatrix 1 -2 1 endbmatrix, eginbmatrix 1 1 4 endbmatrix in mathbbR^3
b) eginbmatrix 1 -1 2 endbmatrix, eginbmatrix 2 0 1 endbmatrix, eginbmatrix -1 2 -1 endbmatrix in mathbbR^3
c) x^3 + 2x^2, -x^2 + 3x + 1, x^3 - x^2 + 2x - 1 in P3(mathbbR)

Added by Christina E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert David Mccaslin

06/29/2022

Step 1

**Step 1:** Set up the matrix with the given vectors as column vectors: \[ \begin{bmatrix} 23 + 222\sqrt{322 + 32 + 1} & 23\sqrt{22 + 21} - 1 \\ 23\sqrt{22 + 21} - 1 & 0 \end{bmatrix} \] **Step 2:** Perform row operations to check for linear independence: Show more…

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