What must be the matrix X, if 2x +\(\begin{bmatrix} 1& 2 \\ 3 & 4 \end{bmatrix}=\begin{bmatrix} 3 & 8 \\ 7 & 2 \end{bmatrix}?\)

(a)

\(\begin{bmatrix} 1& 3 \\ 2 &-1 \end{bmatrix}\)

(b)

\(\begin{bmatrix} 1& -3 \\ 2 &-1 \end{bmatrix}\)

(c)

\(\begin{bmatrix} 2& 6 \\ 4 &-2 \end{bmatrix}\)

(d)

\(\begin{bmatrix} 2& -6 \\ 4 &-2 \end{bmatrix}\)

If the points (x,−2), (5, 2), (8, 8) are collinear, then x is equal to

(a)

-3

(b)

\({1\over 3}\)

(c)

1

(d)

3

If the square of the matrix \(\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}\) is the unit matrix of order 2, then \(\alpha ,\beta \) and \(\gamma\) should satisfy the relation.

(a)

1 + \(\alpha ^2+\beta \gamma=0\)

(b)

1 - \(\alpha ^2-\beta \gamma=0\)

(c)

1 - \(\alpha ^2+\beta \gamma=0\)

(d)

1 + \(\alpha ^2-\beta \gamma=0\)

If A is skew-symmetric of order n and C is a column matrix of order n \(\times\) 1, then C^T AC is

(a)

an identity matrix of order n

(b)

an identity matrix of order 1

(c)

a zero matrix of order 1

(d)

an identity matrix of order 2

If A(B + C) = AB + AC where A, B, C are matrices of the same order than the property applied is matrix multipication is _______ .

(a)

commutative

(b)

association

(c)

distributive over addition

(d)

distributive over multiplication

The product of any matrix by the scalar_________is the null matrix.

(a)

1

(b)

0

(c)

I

(d)

matrix itself

If A is a matrix 3 \(\times\) 3, then \({ { (A }^{ 2 }) }^{ -1 }\) =____________

(a)

\(\frac { 1 }{ { A }^{ 2 } } \)

(b)

A^-2

(c)

\({ { (A }^{ -1 }) }^{ 2 }\)

(d)

I

If \(\left( \begin{matrix} 2 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3 \end{matrix} \right) \) is a singular matrix, then \(\lambda \) is_____________

(a)

\(\lambda \)=2

(b)

\(\lambda \)≠2

(c)

\(\lambda =\frac { -8 }{ 5 } \)

(d)

\(\lambda \neq \frac { -8 }{ 5 } \)

Choose the incorrect statement

(a)

Matrix multiplication is non commutative

(b)

Matrix addition is associative

(c)

Singular matrices have inverse

(d)

Non singular matrices have inverse

If \(\begin{bmatrix} 4 & 3 \\ -2 & x \end{bmatrix}\) is singular then the value of x is _____________

(a)

\(\frac{3}{2}\)

(b)

-\(\frac{3}{2}\)

(c)

3

(d)

-2