(a) Consider the system of linear equations z+y-2z2 11110 2-3 (1) Write down the coefficient matrix A for this system. (

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A Consider The System Of Linear Equations Z Y 2z2 11110 2 3 1 Write Down The Coefficient Matrix A For This System 1 (42.07 KiB) Viewed 29 times

(a) Consider the system of linear equations z+y-2z2 11110 2-3 (1) 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 ER and B = 1 + t² t² 0 -2 2 t (i) Show that det (B) = t(t+1)(t-1). (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, ER such that x is a A-eigenvector of A and x is a 4-eigenvector of B. Prove that A is an eigenvalue of the matrix AB