Question: 2. A linear system is given as where Ax = b 2 1 0 x b Aa 4 3a X = X2 00 2

2. A linear system is given as where Ax = b 2

2. A linear system is given as where Ax = b 2 1 0 x b Aa 4 3a X = X2 00 2 X3 b= b by (a) Use elementary row operations to determine the rank of the matrix A if (i) a=22 (ii) a=4 Hence, determine the condition imposed on a so that a unique solution can be obtained for any vector b. (10 Marks) (b) (i) Determine the eigenvalues of matrix A in terms of a. (ii) Determine the eigenvectors for the case of a = 3. (11 Marks)

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