16. Given real numbers a.b, and c, find x,y, and z that guarantee that the matrix 11 is singular,...

Question

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 18. Let v = 1 and let A = I — tmT. Find the eigenvalues and eigenvectors 1
a b a — b 13= b c b-i-c x y z
[2 1
so that A has eigenvectors (3,1) and
of A.

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Robert · Accepted Answer

//// Solution to the problem number 15 :- 
| 1  1  1  1 | 
 | 1  1 -1 -1 | 
A1 =  | 1 -1  1 -1 | 
   | 1 -1 -1  1 | 
------------------------------------------------------------------------ 
 | 1  0  0  0 | 
 | 0  2  0  0 | 
A2 =  | 0  0  3  0 | 
   | 0  0  0  0 | 
--------------------------------------------------------------------- 
 | 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.

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...

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