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Extended Answer Question 2 (a) Consider the system of linear equations x + 2y z = 0 y+z=1 z = 3 (i) Write down the coefficient matrix A for this system. (That is, write down the matrix A so that this system has augmented matrix [A | b].) (ii) Find the inverse of the matrix A from part (i). (iii) Use A-¹ to find the solution to this system. 1 B = t -t 3 -t t+1 -2 1 0 t-1 (i) Show that det (B) = (t + 7). (ii) Use part (i) to write down the values of t for which B does not have an inverse. (c) Let A and B ben x n matrices. Suppose there is a vector x 0 and scalars A, μER such that x is a A-eigenvector of A and x is a μ-eigenvector of B. Prove that λ + is an eigenvalue of the matrix A + B (b) Lett E R and

Extended Answer Question 2 (a) Consider the system of linear equations x + 2y z = 0 y+z=1 z = 3 (i) Write down the coefficient matrix A for this system. (That is, write down the matrix A so that this system has augmented matrix [A | b].) (ii) Find the inverse of the matrix A from part (i). (iii) Use A-¹ to find the solution to this system. 1 B = t -t 3 -t t+1 -2 1 0 t-1 (i) Show that det (B) = (t + 7). (ii) Use part (i) to write down the values of t for which B does not have an inverse. (c) Let A and B ben x n matrices. Suppose there is a vector x 0 and scalars A, μER such that x is a A-eigenvector of A and x is a μ-eigenvector of B. Prove that λ + is an eigenvalue of the matrix A + B (b) Lett E R and

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Extended Answer Question 2 (a) Consider the system of linear equations x+2y-z = 0 y+z=1 z = 3 (i) Write down the coefficient matrix A for this system. (That is, write down the matrix A so that this system has augmented matrix [A | b].) (ii) Find the inverse of the matrix A from part (i). (iii) Use A-¹ to find the solution to this system. (b) Lett E R and B = t -t 3 -t t+1 -2 1 0 t-1 (i) Show that det (B) = (t + 7). (ii) Use part (i) to write down the values of t for which B does not have an inverse. (c) Let A and B be n x n matrices. Suppose there is a vector x 0 and scalars A, μER such that x is a A-eigenvector of A and x is a μ-eigenvector of B. Prove that λ + is an eigenvalue of the matrix A + B
Transcribed Image Text:Extended Answer Question 2 (a) Consider the system of linear equations x+2y-z = 0 y+z=1 z = 3 (i) Write down the coefficient matrix A for this system. (That is, write down the matrix A so that this system has augmented matrix [A | b].) (ii) Find the inverse of the matrix A from part (i). (iii) Use A-¹ to find the solution to this system. (b) Lett E R and B = t -t 3 -t t+1 -2 1 0 t-1 (i) Show that det (B) = (t + 7). (ii) Use part (i) to write down the values of t for which B does not have an inverse. (c) Let A and B be n x n matrices. Suppose there is a vector x 0 and scalars A, μER such that x is a A-eigenvector of A and x is a μ-eigenvector of B. Prove that λ + is an eigenvalue of the matrix A + B
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