Let a1=[15−1], a2=[−6−262], and b=[59h]. For what value(s) of h is b in the plane spanned by a1 and a2?

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gamau6v

Answered question

2021-11-22

Let $a_{1} = [\begin{matrix} 1 \\ 5 \\ - 1 \end{matrix}], a_{2} = [\begin{matrix} - 6 \\ - 26 \\ 2 \end{matrix}]$ , and $b = [\begin{matrix} 5 \\ 9 \\ h \end{matrix}]$ . For what value(s) of h is b in the plane spanned by $a_{1}$ and $a_{2}$ ?

Answer & Explanation

Ralph Lester

Beginner2021-11-23Added 16 answers

Given:

a_{1} = [\begin{matrix} 1 \\ 5 \\ - 1 \end{matrix}], a_{2} = [\begin{matrix} - 6 \\ - 26 \\ 2 \end{matrix}], a n d b = [\begin{matrix} 5 \\ 9 \\ h \end{matrix}]

To find value of h if b spanned by

a_{1}

and

a_{2}

Since b is spanned by

a_{1}

and

a_{2}

α (1, 5, - 1) + β (- 6, - 26, 2) = (5, 9, h)

α - 6 β = 9

5 α - 26 β = 9

- α + 2 β = h

Solving first two equation, we get

α = - 19, β = - 4

h = 11

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