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(a) By using the fact that M is an upper triangular matrix, calculate det M, clearly stating any theorem you make use of in deducing your answer. How does this imply that M is invertible? (b) Use the method from lectures for the computation of matrix inverses to calculate M-1.

(a) By using the fact that M is an upper triangular matrix, calculate det M, clearly stating any theorem you make use of in deducing your answer. How does this imply that M is invertible? (b) Use the method from lectures for the computation of matrix inverses to calculate M-1.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.1: Orthogonality In Rn
Problem 28EQ
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Please do parts a, b, c, d

1. . Let m12, m13, m23 E R. Consider the matrix [1 1 m12 m13 M = 1 т23 (a) By using the fact that M is an upper triangular matrix, calculate det M, clearly stating any theorem you make use of in deducing your answer. How does this imply that M is invertible? (b) Use the method from lectures for the computation of matrix inverses to calculate M-1. (c) A single word of nine letters is written in terms of numbers by the correspondence A + 1, B + 2 etc. The word is then made into a 3 x 3 matrix by placing it down columns in order, and then encrypted by multiplication on the left by the matrix M with m12 = -3, -101 what was the original 17 34 m13 = 2, m23 = -2. If the encrypted matrix is -19 -31 2 14 16 word? You may make use of Matlab to carry out the required matrix multiplication. (d) From your answer to (a), specify 3 x 3 elementary matrices E1, E2, E3 such that M-1 = E3E2Ei.
Transcribed Image Text:1. . Let m12, m13, m23 E R. Consider the matrix [1 1 m12 m13 M = 1 т23 (a) By using the fact that M is an upper triangular matrix, calculate det M, clearly stating any theorem you make use of in deducing your answer. How does this imply that M is invertible? (b) Use the method from lectures for the computation of matrix inverses to calculate M-1. (c) A single word of nine letters is written in terms of numbers by the correspondence A + 1, B + 2 etc. The word is then made into a 3 x 3 matrix by placing it down columns in order, and then encrypted by multiplication on the left by the matrix M with m12 = -3, -101 what was the original 17 34 m13 = 2, m23 = -2. If the encrypted matrix is -19 -31 2 14 16 word? You may make use of Matlab to carry out the required matrix multiplication. (d) From your answer to (a), specify 3 x 3 elementary matrices E1, E2, E3 such that M-1 = E3E2Ei.
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