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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.

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 is:
Q. The Eigen value of the matrix eigen value of matrix
Q. The Eigen values of a skew-symmetric matrices are?
Q. The Eigen value of the 2 x 2 matrix eigen value of matrix are __________?

Q. Let eigen value of matrix example be a matrix then the Eigen values of A9 will be?
Q. Consider for a matrix A = example of matrix, 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. The matrix discrete mathematics matrix is
Q. Let A = matrix example discrete mathematics 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 is 168. Then the determinant of the matrix matrix example discrete mathematics will be?

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