Question 3 (35 marks) Let A = where h real constant: Find the inverse of by using the inversion algorithm. the adjoint method (b) Use the matrix inverse method and the result of (a) to solve each of the following linear systems_ 2xj 4x2 2xz 2x; R+I. R+l 2x; Xz; 3x, 3x; R+3. Use Cramer $ rule to solve the system of linear equations in (b)(ii). Let B be a 3x3 matrix such that det(B)= R+2. Find the following in terms of h. det (34*B" det (adj( AB))
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Matrix A is given as: $$ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & h & 6 \\ 7 & 8 & 9 \end{bmatrix} $$ Show more…
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Question 3 Let A = [1 2 0; 1 1 h; 0 h 1], where h is a real constant. (a) Find the inverse of A by using (i) the inversion algorithm. (ii) the adjoint method. (b) Use the matrix inverse method and the result of (a) to solve each of the following linear systems. (i) 2x1 + 4x2 = -2, 2x2 - x3 = 1, x1 + x2 - 2x3 = R+1. (ii) x1 + x2 = R+1, 2x1 + x2 + 3x3 = 2, 3x2 + x3 = R+3. (c) Use Cramer's rule to solve the system of linear equations in (b)(ii). (d) Let B be a 3x3 matrix such that det(B) = R+2. Find the following in terms of h. (i) det(3A^2B^T) (ii) det(adj(AB))
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Consider the matrix A = (i) Find the adjoint matrix of A. (ii) Use the adjoint method to find the inverse of matrix A. (iii) Hence, solve the following system of linear equations. x + 2y - z = 6 3x + y - z = 10 2x - 2y = 2 (b) Given that A, B and C are 3x3 matrices where det(A) = 2, det(B) = 4 and det(C) = 7. Compute the following determinant.
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