Let A E M₁ (R) be the matrix d₁ d₂ d3 d₁ 0 1 1 1 A: 1 0 1 1 1 1 0 1 where the first row consists of these numbers: 2,2,1,7 (a) Compute the determinant det(A). In order to get full marks you must show your working. (b) Decide whether or not A is invertible. (c) Is the solution of the homogeneous linear system with coefficient matrix A unique? Justify your answer.

4. Let two 3 × 3 matrices A and B be given by 1 -2 2 0 1 -1 A = -2 1 0 and B = -5 1 -3 3 3 -2 -1 (a) Calculate the matrix products AB and A'B, where A' is the transpose of A. (b) Calculate the determinants of A and B. Use the result to obtain the determinant of AB and of A'B. (c) Calculate the inverse matrix of A, if it exists.