Given x1 = 1 -1 2 and x2 = 3 1 1 .

May 7, 2026Mathematics

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May 7, 2026

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k x_1$ for some scalar $k$:

Step 1: Determine linear independence for 4.1.1. A set of two vectors is linearly dependent if and only if one vector is a scalar multiple of the other. Given $x_1 = \begin{bmatrix} 1 \\ -1 \\ 2 \end{bmatrix}$ and $x_2 = \begin{bmatrix} 3 \\ 1 \\ 1 \end{bmatrix}$ . If $x_2 = k x_1$ for some scalar $k$ : From the first component: $3 = k \cdot 1 \implies k = 3$ . From the second component: $1 = k \cdot (-1) \implies k = -1$ . Since the value of $k$ is not consistent, $x

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Determine linear independence for 4.1.1. A set of two vectors is linearly dependent if and only if one vector is a scalar multiple of the other.

Asked on May 7, 2026Mathematics

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ScanSolve AI AnswerAnswered on May 7, 2026

Step 1: Determine linear independence for 4.1.1. A set of two vectors is linearly dependent if and only if one vector is a scalar multiple of the other. Given x_1 = 1 \\ -1 \\ 2 and x_2 = 3 \\ 1 \\ 1 . If x_2 = k x_1 for some scalar k: From the first component: 3 = k · 1 k = 3. From the second component: 1 = k · (-1) k = -1. Since the value of k is not consistent, $x