16. Given real numbers a.b, and c, find x,y, and z that guarantee that the matrix 11 is singular, with real eigenvalues. and with three orthogonal eigenvectors 17. Complete the matrix A = (2.1). [1...

//// Solution to the problem number 15 :-
| 1 1 1 1 |
| 1 1 -1 -1 |
A1 = | 1 -1 1 -1 |
| 1 -1 -1 1 |
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| 1 0 0 0 |
| 0 2 0 0 |
A2 = | 0 0 3 0 |
| 0 0 0 0 |
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| 1 0 0 0 |
| 0 1 0 0 |
A3 = | 0 0 1 -1 |
| 0 0 1 1 |
A = A1 * A2 * A3.
So, after multiplying all these matrices, we will have the value of matrix, A as follows :-
| 1 2 3 -3 |
| 1 2 -3 3 |
A = | 1 -2 3 -3 |
| 1 -2 -3 3 |
Now let us reduce this above matric to its echelon form,
=> R4 = R3 - R4.
| 1 2 3 -3 |
| 1 2 -3 ...