MATHS RIVER

Numerical Integration part i

Applications of Derivatives

Exact Differential Equation

Cyclic Groups

Cosets and Lagranges Theorem

Eigenvalues and Eigenvectors

Q. 5
If A and B are square matrices of same order and B is a skew symmetric matrix, then A'BA is
(a) Null matrix
(b) Diagonal matrix
(c) Skew symmetric matrix
(d) Symmetric matrix

Q. 4
If P and Q are symmetric matrices of the same order then PQ – QP is
(a) identity matrix
(b) zero matrix
(c) symmetric matrix
(d) skew symmetric matrix

Q.3
Let M be 2 × 2 symmetric matrix with integer
entries, then M is invertible if

(a) the first column of M is the transpose of
second row of M
(b) the second row of M is the transpose of first column of M
(c) M is diagonal matrix with non-zero entries in the principal diagonal
(d) the product of entries in the principal diagonal of M is the product of entries in the other diagonal

2.
The set of all 2×2 matrices over the real
numbers is not a group under matrix
multiplication because :
(a) identity element does not exist
(b) closure property is not satisfied
(c) association property is not satisfied
(d) Inverse axiom may not be satisfied