Question

Find the vector in the subspace $W$ spanned by $\begin{Bmatrix} \begin{bmatrix} -4 \\ 4 \\ 3 \\ -3 \end{bmatrix}, \begin{bmatrix} -2 \\ 4 \\ -4 \\ 1 \end{bmatrix} \end{Bmatrix}$ which is closest to $\begin{bmatrix} -24 \\ 27 \\ -2 \\ -8 \end{bmatrix}$. Answer:

Name: find the vector in the subspace w spanned by beginbmatrix beginbmatrix 4 4 3 3 endbmatrix beginbmatrix 2 4 4 1 endbmatrix endbmatrix which is closest to beginbmatrix 24 27 2 8 endbmatrix ans 99713
Uploaded: 2023-08-21T14:11:58-08:00
Duration: 3 min 36 s
Channel: Sri K
Description: find the vector in the subspace w spanned by beginbmatrix beginbmatrix 4 4 3 3 endbmatrix beginbmatrix 2 4 4 1 endbmatrix endbmatrix which is closest to beginbmatrix 24 27 2 8 endbmatrix ans 99713

          Find the vector in the subspace $W$ spanned by $\begin{Bmatrix} \begin{bmatrix} -4 \\ 4 \\ 3 \\ -3 \end{bmatrix}, \begin{bmatrix} -2 \\ 4 \\ -4 \\ 1 \end{bmatrix} \end{Bmatrix}$ which is closest to $\begin{bmatrix} -24 \\ 27 \\ -2 \\ -8 \end{bmatrix}$.
Answer:

find the vector in the subspace w spanned by beginbmatrix beginbmatrix 4 4 3 3 endbmatrix beginbmatrix 2 4 4 1 endbmatrix endbmatrix which is closest to beginbmatrix 24 27 2 8 endbmatrix ans 99713

Added by Sarah J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

08/21/2023

Step 1

Let $b = \begin{bmatrix} -24 \\ 27 \\ -2 \\ -8 \end{bmatrix}$. We want to find the projection of $b$ onto the subspace $W$ spanned by $v_1$ and $v_2$. First, we check if $v_1$ and $v_2$ are orthogonal. $v_1 \cdot v_2 = (-4)(-2) + (4)(4) + (3)(-4) + (-3)(1) = 8 + Show more…

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Find the vector in the subspace $W$ spanned by $\begin{Bmatrix} \begin{bmatrix} -4 \\ 4 \\ 3 \\ -3 \end{bmatrix}, \begin{bmatrix} -2 \\ 4 \\ -4 \\ 1 \end{bmatrix} \end{Bmatrix}$ which is closest to $\begin{bmatrix} -24 \\ 27 \\ -2 \\ -8 \end{bmatrix}$. Answer: