1st Year Mathematics Chapter 4 TestUNIT 4: Matrices and Determinants

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

1. The (0,0) solution of the system a₁x+b₁y=0 and a₂x+b₂y=0 is called ......:

   1. Consistent

   2. Inconsistent

   3. Non-trivial

   4. Trivial

2. For homogeneous linear equations, system AX=0 non-trivial solution is possible if IAI = ......:

   1. Non-zero

   2. Zero

   3. Negative

   4. Positive

3. The inverse of a square matrix exists if A is:

   1. Singular

   2. Non singular

   3. Symmetric

   4. Rectangular

4. The trivial solution of homegeneous linear equation isL

   1. (1,0,0)

   2. (0,1,0)

   3. (0,0,1)

   4. (0,0,0)

5. If order of a matrix A is m x n, then the order of A^t is ......:

   1. m x n

   2. n x n

   3. n x m

   4. m x m

6. The matrix  is ......:

   1. Non-singular

   2. Symmetric

   3. Skew symmetric

   4. Singular

7. If A is a matrix of order 3 x 2 then order of A^tA is ......:

   1. 3 x 2

   2. 2 x 3

   3. 2 x 2

   4. 3 x 3

8. If A and B are square matrices of the same order than ......:

   1. (A+B)²=A²+2AB+B²

   2. (A+B)²=A²+2B A+B²

   3. Both a and b

   4. None of these

9. If AX=B represent the system of non-homogenous linear equation then X=......:

   1. BA^-1

   2. AB

   3. A^-1B^-1

   4. A^-1B

10. If A is a square matrix of order 3 x 3 then IKAI=......:

    1. KIAI

    2. k²IAI

    3. k³ IAI

    4. k IAI³