Question: please show all the details Problem 1 (15 points): (a) Prove a triangular matrix with nonzero diagonal entries is non-singular. (b) Let q1, 92, .

please show all the details

Problem 1 (15 points): (a) Prove a triangular matrix with nonzero diagonal entries is non-singular. (b) Let q1, 92, . . . , qk be orthonormal vectors in Cm and define a matrix Q to be the matrix whose columns are q; for j = 1, . . . , k . If P := QQ*, show that I - P is orthogonal projection. . For each j = 1, . . . , k define Plq; = I - qiq*. Show that P = II;_1 Pla

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