[Solved]10 Matrix C Ata 1 E Rn N Rank N Assume Thin Qr Decomposi Tion Qr Available Show C Rtr 1 B Q37163715

10. The matrix C = (ATA)-1 E Rn×n, where rank(A) = n. Assume that the thin QR decomposi- tion A QR is available. (a) Show C(RTR)-1 (b) Give an algorithm for computing the diagonal of C that requires about n/3 operations. (c) Show that if R u 61 -Cru/a where C1 (STs)-1 (d) Give an algorithm to compute the upper triangular portion of C that requires about 2n3/3 operations. Show transcribed image text 10. The matrix C = (ATA)-1 E Rn×n, where rank(A) = n. Assume that the thin QR decomposi- tion A QR is available. (a) Show C(RTR)-1 (b) Give an algorithm for computing the diagonal of C that requires about n/3 operations. (c) Show that if R u 61 -Cru/a where C1 (STs)-1 (d) Give an algorithm to compute the upper triangular portion of C that requires about 2n3/3 operations.

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Answer to 10. The matrix C = (ATA)-1 E Rn×n, where rank(A) = n. Assume that the thin QR decomposi- tion A QR is available. (a) Sh… . . .