Q. Which of the following statement is correct?
S1: (diag[X, Y, Z])-1 = diag [1/X, 1/Y, 1/Z] |
S2: Eigen value of diag[X, Y, Z] = X, Y, Z |
S3: Determinant of diag[X, Y, Z] = |diag[X, Y, Z]| = XY+YZ+ZX |
Here diag[X, Y, Z ]
is a diagonal matrix whose diagonal elements are X, Y and Z.
Q. Which of the following matrices is not an idempotent matrix?
Q. Consider a matrix B
is a skew-symmetric matrix. Then B.B
is a __________?
Q. Let A5x7
, B5x7
and C4x7
, be three different matrices. Then the order of (C(ATB)-1CT)T
is __________.
Q. Let A
and B
be two square matrices of order N x N
. Which of the following statement is correct?
S1: tr(A+B) = tr(A) + tr(B) |
S2: tr(AB) ≠ tr(BA) |
S3: If the value of the tr(A) = 5 then the value of tr(A3) = 125 |
Q. The inverse of the matrix of order 2x2
![inverse of matrix](../images/discrete-maths-1-5.png)
is:
Q. The Eigen value of the matrix
![eigen value of matrix](../images/discrete-maths-1-10.png)
Q. The Eigen values of a skew-symmetric matrices are?
Q. The Eigen value of the 2 x 2 matrix
![eigen value of matrix](../images/discrete-maths-1-11.png)
are __________?
Q. Let
![eigen value of matrix example](../images/discrete-maths-1-12.png)
be a matrix then the Eigen values of
A9
will be?
Q. Consider for a matrix A =
![example of matrix](../images/discrete-maths-1-13.png)
,
X
= trace of
A
and
Y
= determinant of
A
. Then the value of
(X2 + Y2)
will be __________.
Q. Let A3x3
and B3x3
are two matrices then the product of matrix B-1(AB-1)-1A
will be?
Q. Let A =
![matrix example discrete mathematics](../images/discrete-maths-1-1-15.png)
be a matrix whose eigen values are
3
and
5
. The value of
X2+XY
will be,
Q. Given that the determinant of the matrix
![matrix example discrete mathematics](../images/discrete-maths-1-16.png)
is 168. Then the determinant of the matrix
![matrix example discrete mathematics](../images/discrete-maths-1-17.png)
will be?