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Question 3 (35 marks) 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))

          Question 3 (35 marks)

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))

Show more…

Question 3 (35 marks)

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))

Added by Amanda Z.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shaiju T

04/06/2022

Step 1

Step 1: Find the inverse of matrix A using the inversion algorithm: Given matrix A: \[ A = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} \] Following the inversion algorithm, perform row operations to reduce A to the identity matrix: \[ A^{-1} 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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