Determine if b is a linear combination of a1, a2, and a3.

Chapter 1, Problem 12E

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QUESTION:

Determine if b is a linear combination of \(\mathbf{a}_{1}, \mathbf{a}_{2}\), and \(\mathbf{a}_{3}\).

\(\mathbf{a}_{1}=\left[\begin{array}{r}
1 \\
-2 \\
2
\end{array}\right], \mathbf{a}_{2}=\left[\begin{array}{l}
0 \\
5 \\
5
\end{array}\right], \mathbf{a}_{3}=\left[\begin{array}{l}
2 \\
0 \\
8
\end{array}\right], \mathbf{b}=\left[\begin{array}{r}
-5 \\
11 \\
-7
\end{array}\right]\)

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QUESTION:

Determine if b is a linear combination of \(\mathbf{a}_{1}, \mathbf{a}_{2}\), and \(\mathbf{a}_{3}\).

\(\mathbf{a}_{1}=\left[\begin{array}{r}
1 \\
-2 \\
2
\end{array}\right], \mathbf{a}_{2}=\left[\begin{array}{l}
0 \\
5 \\
5
\end{array}\right], \mathbf{a}_{3}=\left[\begin{array}{l}
2 \\
0 \\
8
\end{array}\right], \mathbf{b}=\left[\begin{array}{r}
-5 \\
11 \\
-7
\end{array}\right]\)

ANSWER:

Step 1 of 4

Given

\(a_{1}=\left[\begin{array}{c} 1 \\ -2 \\ 2 \end{array}\right] \quad a_{2}=\left[\begin{array}{l} 0 \\ 5 \\ 5 \end{array}\right], \quad a_{3}=\left[\begin{array}{l} 2 \\ 0 \\ 8 \end{array}\right] \quad b=\left[\begin{array}{c} -5 \\ 11 \\ -7 \end{array}\right] \)

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