(a) For each of the following systems; write the matrix equation and the augmented form of...

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(a) For each of the following systems; write the matrix equation and the augmented form of the system but DO NOT solve the system: i. ii. (c) Expand the determinant 2x1 + x2-3x3 = 4 4x1 +2r3 = 10 -2x1 + 3x2 - 13x3 = -8 Т 3 + 4 = ₁ + 2x₂ 2x1 + 4x2 + 3x3 = 5 6x3 +7= 1 + 2x2 +2=4 2x+y+z=7 x+y+22=9 (b) Find the eigenvalues of the orthogonal matrix A = 2 6 2 3 2 3 5 4 2 1 122 4 2 1 -2 1 2 -2 (3 marks) (3 marks) (10 marks) (6 marks) (d) Solve the following system of linear equations by Gauss-Jordan Elimination method: (10 marks) (a) For each of the following systems; write the matrix equation and the augmented form of the system but DO NOT solve the system: i. ii. (c) Expand the determinant 2x1 + x2-3x3 = 4 4x1 +2r3 = 10 -2x1 + 3x2 - 13x3 = -8 Т 3 + 4 = ₁ + 2x₂ 2x1 + 4x2 + 3x3 = 5 6x3 +7= 1 + 2x2 +2=4 2x+y+z=7 x+y+22=9 (b) Find the eigenvalues of the orthogonal matrix A = 2 6 2 3 2 3 5 4 2 1 122 4 2 1 -2 1 2 -2 (3 marks) (3 marks) (10 marks) (6 marks) (d) Solve the following system of linear equations by Gauss-Jordan Elimination method: (10 marks)