Q6 RQ factorization of a wide matrix, projectors Let U R4x4 be an orthogonal matrix....

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Q6 RQ factorization of a wide matrix, projectors Let U € R4x4 be an orthogonal matrix. Consider the matrices -4 -4 10 8 0 -2 9 0 1 0 A := 2 -2, B:= (¹ 8). P= I₁-UBT (BBT)-¹BUT. -4 -4 10 -29 0 (1) Using Householder, find R E R³×4 and Q E R4x4 such that R := (01¹) is upper-triangular, R Q is orthogonal, and RQ = A. (Hint: Find a factorization ARQ of a certain à € R4×4.) (ii) Compute the singular values and the rank of P. (Hint: First, prove P is an orthogonal projector.) Q6 RQ factorization of a wide matrix, projectors Let U € R4x4 be an orthogonal matrix. Consider the matrices -4 -4 10 8 0 -2 9 0 1 0 A := 2 -2, B:= (¹ 8). P= I₁-UBT (BBT)-¹BUT. -4 -4 10 -29 0 (1) Using Householder, find R E R³×4 and Q E R4x4 such that R := (01¹) is upper-triangular, R Q is orthogonal, and RQ = A. (Hint: Find a factorization ARQ of a certain à € R4×4.) (ii) Compute the singular values and the rank of P. (Hint: First, prove P is an orthogonal projector.)