Question: 1. Let a = (5, -8, 0, 3) and b = (0, 2, -4, 3). (a) Calculate (26 - 4a) (b) Calculate (2b - 4a)

1. Let a = (5, -8, 0, 3) and b = (0, 2, -4, 3). (a) Calculate (26 - 4a) (b) Calculate (2b - 4a) . (b + 2a) (c) Calculate || a || and || 6 || (d) Show that the Triangle Inequality applies in this case. 2. Consider the following matrix: -2 1 A = 4 5 3 -2 (a) Calculate the determinant of A. (b) Find the inverse of A, if it exists. 3. Solve the following system of linear equations using matrix inversion: -2x + y + 3z =11 4x + 5y + 3z = 3 x - 2y - z=-6

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