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Matrices and Determinants

Theory and Formula


Question

Q1. Write the number of all possible matrices of order 3 x 3 with each entry 1,2,

(a) 24 (b) 31 (c) 29 (d) 33

Solution.
(c) 29
Solution

Q2. Find the simplified value of 8A - (1 + A)3, if A is a square matrix such that A2 = A .

(a) 2A (b) I + A (c) A (d) A - I

Solution.
(d) A - I
Solution

Q3. Only square matrix have determinants .

(a) True (b) False (c) Can't say

Solution.
(a) True
Solution

Q4. If matrix are equal matix .

(a) Their order will be same
(b) Corresponding element should be same
(c) Both a and b
(d) None of these

Solution.
(c) Both a and b
Solution

Q5. Two matrix A and B having order (2 x 3) and (3 x 1) then which product is possible.

(a) AB (b) BA (c) Both (d) None

Solution.
(a) AB
Solution

Q6. If A is square matrix of order (3 x 3) then find the value of k if I3AI = kIAI .

(a) 9 (b) 3 (c) 27 (d) 81

Solution.
(c) 27
Solution

Q7. a11A11 + a12A12 + a13A13 = ___________ .

Solution.
Determinant of A(det A)
Solution

Q8. If A is square matrix of order (3 x 3) then find the value of k if I2AI = kIAI

(a) 1 (b) 2 (c) 4 (d) 8

Solution.
(d) 8
Solution

Q9. Which one is incorrect .

(a) (A + B)' = B' + A'
(b) (A')' = A
(c) I2 = I
(d) (AB)' = A'B'

Solution.
(d) (AB)' = A'B'
Solution

Q10. If a matrix has 7 elements then write all possible orders it can have

(a) (7 x 1)(1 x 7) (b) (1 x 7) (c) (7 x 1) (d) (7 x 7)

Solution.
(a) (7 x 1)(1 x 7)
Solution