Question

2. Given the subspace $$S = \left\{ \begin{bmatrix} a-b \\ b-c \\ c-a \end{bmatrix} | a, b, c \in \mathbb{R} \right\}$$ of $$\mathbb{R}^3$$, find a basis for $$S$$.

Name: 2 given the subspace s left beginbmatrix a b b c c a endbmatrix a b c in mathbbr right of mathbbr3 find a basis for s 25573
Uploaded: 2022-06-06T09:20:34-08:00
Duration: 2 min 14 s
Channel: Ben Blakesley
Description: 2 given the subspace s left beginbmatrix a b b c c a endbmatrix a b c in mathbbr right of mathbbr3 find a basis for s 25573

          2. Given the subspace $$S = \left\{ \begin{bmatrix} a-b \\ b-c \\ c-a \end{bmatrix} | a, b, c \in \mathbb{R} \right\}$$ of $$\mathbb{R}^3$$, find a basis for $$S$$.

Added by Joseph K.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ben Blakesley

06/06/2022

Step 1

Step 1: We can rewrite the vector as a linear combination of vectors with coefficients a, b, and c: $$ \begin{bmatrix} a-b \\ b-c \\ c-a \end{bmatrix} = a \begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix} + b \begin{bmatrix} -1 \\ 1 \\ 0 \end{bmatrix} + c \begin{bmatrix} Show more…

Show all steps

Thanks for your feedback!

2. Given the subspace $$S = \left\{ \begin{bmatrix} a-b \\ b-c \\ c-a \end{bmatrix} | a, b, c \in \mathbb{R} \right\}$$ of $$\mathbb{R}^3$$, find a basis for $$S$$.