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  3. consider an orthogonal matrix q ∈ r ^m×m

Consider an orthogonal matrix Q ∈ R ^m×m and a diagonal matrix with non-zero diagonal elements...

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Advance Math

Consider an orthogonal matrix Q ∈ R ^m×m and a diagonal matrixwith non-zero diagonal elements D ∈ R^ m×m and answer the True—False questions below.

(k) Any vector x ∈ R^m can be written as a linear combination ofthe columns of D

(l) The columns of Q span R^m

(m) The columns of D span R^m

(n) The columns of Q are a basis for R^m

(o) The columns of D are a basis for R^m

Answer & Explanation Solved by verified expert
3.8 Ratings (470 Votes)
k Since the diagonal entries in are nonzero thecolumns are nonzero multiples of the standard basis vectorsTherefore they form a basis of Inparticular canbe written as a linear combination    See Answer
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