Q. Let a matrix A =
then the sum of elements of middle row of
A-1 will be __________.
Q. Let a matrix A =
, then A will be, __________.
Q. If a matrix A =
is not invertible then the value of
"p" will be __________.
Q. The inverse of the matrix
is __________.
Q. Match the column I with column II and choose the correct option.
| Column I | Column II |
|---|
| A. Orthogonal matrix | 1) determinant=0 |
| B. Singular matrix | 2) determinant = always 1. |
| C. Real symmetric matrix | 3) Eigen values are always real. |
| D. Non-singular matrix | 4) Eigen values are not defined. |
| 5) determinant is not defined. |
|
|
|
|
|
|
Q. The rank of matrix A =
is __________.
Q. The rank of the matrix
is __________. Here
x and
y are integers and
x lies between
1 and
10 and
y lies between
-10 and
10. Choose the most correct option.
Q. The following system of homogenous equation has non-trivial solution then value of "p" is __________.
3x + 2y + pz = 0
4x - 2y + 6z = 0
5x + y = 0
Q. If the determinant of a matrix is equal to 12 and one of the eigen value is also equal to 12. Then one eigen value of adj(A) will be equal to __________.
Q. The sum of the eigen values of a given matrix A =
is __________.
Q. Which of the following statements is/are not correct?
| (i) Sum of eigen values of matrix A is equal to trace of matrix. |
| (ii) Product of eigen values of matrix A is equal to determinant of matrix A |
| (iii) For singular matrix, atleast one eigen value is equal to 0. |
| (iv) Similar matrices have different eigen values. |
Q. For a given matrix A =
One of the eigen value is
-5. The other two eigen values are __________.
Q. The eigen values of a matrix A =
will be __________.
