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Discrete Maths Test 2

This Test will cover complete Discrete Mathematics with very important questions, starting off from basics to advanced level.
Q. Let a matrix A = example of matrix discrete mathematics then the sum of elements of middle row of A-1 will be __________.
Q. Let a matrix A = example of matrix discrete mathematics, then A will be, __________.
Q. Let A = example of matrix discrete mathematics and A-1 = example of matrix discrete mathematics then the product of A and A-1 will be __________.
Q. If a matrix A =matrix discrete mathematics is not invertible then the value of "p" will be __________.

Q. The inverse of the matrix matrix discrete mathematics is __________.
Q. The matrix matrix discrete mathematics is a __________.
Q. Match the column I with column II and choose the correct option.
Column IColumn II
A. Orthogonal matrix1) determinant=0
B. Singular matrix2) determinant = always 1.
C. Real symmetric matrix3) Eigen values are always real.
D. Non-singular matrix4) Eigen values are not defined.
5) determinant is not defined.
Q. The rank of matrix A = matrix discrete mathematics is __________.
Q. The rank of the matrix matrix discrete mathematics 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 = matrix discrete mathematics 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 = matrix discrete mathematics One of the eigen value is -5. The other two eigen values are __________.
Q. The eigen values of a matrix A = matrix discrete mathematics will be __________.

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