# Find an orthogonal basis for the column space

When you try to Find an orthogonal basis for the column space, there are often multiple ways to approach it.

Solve Now ## Find an orthogonal basis for the column space of each matrix

You can obtain an orthonormal basis by applying, for instance, Gram-Schmidt to these two vectors. I have to find an orthogonal Basis for the Column Space of \$A\$, where: \$\$A

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## Linear Algebra (Math 2890) Solution to Final Review

Expert Answer escumantsu Answered 2021-09-22 Author has 98 answers Use Gram-Schmidt process to orthogonalize column vectors of A v 1 = x 1 = [ 3 1 − 1 3] v 2 = x 2 − x 2 ⋅ v 1 v 1 ⋅ v 1

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I enjoy doing mathematical equations because they help me to think logically and critically. ## Finding an orthogonal basis from a column space

So you first basis vector is u 1 = v 1 Now you want to calculate a vector u 2 that is orthogonal to this u 1. Gram Schmidt tells you that you receive such a vector by u 2 = v 2 − proj u 1 ( v 2) And

## exam2soln.pdf

Find an orthogonal basis for the column space of the matrix given below: [ 1 2 3 − 3] Here: A = B = So: v 1 = A = And: P r o j v 1 ( B) = ⋅ < 1