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# Discrete Mathematics Test 1

This is not a section-wise test, and will contain questions from the complete curriculum of Discrete Mathematics subject. Enjoy!
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.

 A. S1 and S2 both are true B. Only S2 is true. C. S2 and S3 both are true. D. Only S3 is true.
Q. Which of the following matrices is not an idempotent matrix?
 A. B. C. D.
Q. Consider a matrix `B` is a skew-symmetric matrix. Then `B.B` is a __________?
 A. Diagonal matrix B. Symmetric matrix C. Skew-symmetric matrix D. None of these.
Q. Let `A5x7`, `B5x7` and `C4x7`, be three different matrices. Then the order of `(C(ATB)-1CT)T` is __________.
 A. 7 x 7 B. 4 x 4 C. 4 x 5 D. 5 x 7

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`
 A. S1 and S2 are true B. Only S1 is true C. Both S1 and S3 are true D. All are false
Q. The inverse of the matrix of order 2x2 is:
 A. B. C. D.
Q. The Eigen value of the matrix
 A. 3, 4 and 1 B. 1, 5 and 6 C. 3, 5 and -1 D. 3, 5 and 2
Q. The Eigen values of a skew-symmetric matrices are?
 A. Always purely real B. Real and positive C. Either purely imaginary or zero D. Purely real and negative
Q. The Eigen value of the 2 x 2 matrix are __________?
 A. -1 and 5 B. 1 and -5 C. -5 and -1 D. 5 and 2

Q. Let be a matrix then the Eigen values of `A9` will be?
 A. 1 and 16root2 B. 1 and 512 C. 1 and 32 D. cannot be determined.
Q. Consider for a matrix A = , `X` = trace of `A` and `Y` = determinant of `A`. Then the value of `(X2 + Y2)` will be __________.
 A. 900 B. 1000 C. 100 D. None of the above
Q. Let `A3x3` and `B3x3` are two matrices then the product of matrix `B-1(AB-1)-1A` will be?
 A. `A-1` B. `B-1` C. `I3X3`, here I is an identity matrix D. None of these.
Q. The matrix is
 A. An Idempotent matrix B. An Involutory matrix C. A symmetric matrix D. A skew-symmetric matrix
Q. Let A = be a matrix whose eigen values are `3` and `5`. The value of `X2+XY` will be,
 A. 4 B. 6 C. 5 D. 8
Q. Given that the determinant of the matrix is 168. Then the determinant of the matrix will be?
 A. 84 B. -21 C. -84 D. 21