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
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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
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