Find an orthonormal basis for the subspace U of M2,2(R) spanned by −1 0 1 1 ,  0 1 1 0 .

Question

Find an orthonormal basis for the subspace U of M2,2(R) spanned by −1 0 1 1 ,  0 1 1 0 .
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Solution 1

The given vectors are:

A = [ -1 0 1 1 ]

B = [ 0 1 1 0 ]

Step 1: Check if the vectors are orthogonal

Two vectors are orthogonal if their dot product is zero. In the case of matrices, we use the Frobenius inner product, which is the sum of the products of the corresponding entries.

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