Q. Let
X be a positive integer and matrix A =
If
|adj (A)| = X6. Then the value of
X will be __________.
Q. The maximum no. of different possible non-zero entries in a skew-symmetric matrix of order 11 is __________.
Q. The value of the determinant
is __________.
Q. The sum of minimum and maximum value of a determinant of second order whose elements are either 0 or 1 is equal to __________.
Q. If A =
then the value of the determinant of
[ A2+2A-3I ] will be equal to __________.
Q. For a matrix A =
one of the eigen value is
+3 then which of the following is an eigen vector?
Q. For what values of α and β, the following simultaneous equations have an infinite no. of solutions?
X + Y + Z = 5
X + 3Y + 3Z = 9
X + 2Y + αZ = β
Q. For the homogenous system of linear equation, AX = 0, if the rank of matrix A is equal to no. of unknowns variable then it has __________.
Q. Which of the following option is correct?
| S1: Sum of the eigen values of a matrix = trace of a matrix. |
| S2: For singular matrices, atleast one of the eigen value = 0. |
| S3: The determinant of involutory matrix is either +1 or -1. |
Q. The trace of a matrix is 9 and the determinant of that matrix is 24. Then the eigen values for that matrix will be __________.
Q. A is a 4 x 5 real matrix and AX = B is an inconsistent system of equation. The highest possible rank of A will be __________.
Q. Let a matrix A =
has one eigen value, which is
4. The sum of other two eigen values is __________.
Q. One of the eigen vector of the matrix A =
is __________.
Q. The eigen vectors of matrix A =
are __________.
