Question

Find the orthogonal projection of the vector v = [2 1 -1] onto the subspace spanned by the two vectors a1 = [1 0 1] a2 = [1 1 0]

          Find the orthogonal projection of the vector
v = [2 1 -1]
onto the subspace spanned by the two vectors
a1 = [1 0 1] a2 = [1 1 0]

Added by Todd B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sam Stansfield

04/11/2023

Step 1

Since the given vectors are linearly independent, they form a basis for the subspace. So, the basis is: $$ \begin{bmatrix} 1 \\ 0 \end{bmatrix}, \begin{bmatrix} 0 \\ 1 \end{bmatrix} $$ Now, let's find the orthogonal projection of the vector $\begin{bmatrix} 2 \\ Show more…

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