Matrices and Determinants
1) Which one of the following is 4 × 1 matrices?
- d
- b
- c
- a
Answer: b
2) Find x, y, z, w.
- (3, 4, 3, 2)
- (-1, -2, -3, -4)
- (1, -2, 3, -4)
- (1, 2, 3, 4)
Answer: (1, 2, 3, 4)
3) Find x and y.
- c
- d
- b
- a
Answer: a
4) Find a matrix x such that
- b
- c
- d
- a
Answer: d
5) If A = diag (2, -5, 9) B = diag (1, 1, -4) C = diag (-6, 3, 4), find A - 2B.
- diag (15, -7, 17)
- diag (8, -2, 5)
- diag (0, -7, 17)
- diag (-9, 14, -8)
Answer: diag (0, -7, 17)
6) Find the value of x, y, z [xy + 2z - 3] + [y 4 5] = [4 9 12]
- (1, -3, 10)
- (1, 3, 10)
- (-1, -3 , -10)
- (1, 3, -10)
Answer: (1, 3, 10)
7) Find AB.
- a
- d
- b
- c
Answer: a
8) Find the values x, if A² = B.
- (±1, 4)
- (±1, -4)
- (±2, 4)
- (±3, 4)
Answer: (±1, 4)
9) Find Transpose of A.
- b
- c
- d
- a
Answer: c
10) Find the values of a and b.
- (-4, -2)
- (4, 2)
- (-4, 2)
- (4, -2)
Answer: (4, 2)
11) For what values of x and y the following matrices are equal.
- (2, 4)
- (2, 2)
- (2, 3)
- (-2, 2)
Answer: (2, 2)
12) Find the value of x such that
- (-2, -14)
- (2, -14)
- (2, 14)
- (-2, 14)
Answer: (-2, -14)
13) Find the product of the matrices
- b
- a
- d
- c
Answer: d
14) Find a matrix D such that CD - AB = 0
- d
- b
- a
- c
Answer: a
15) Find A
- c
- d
- b
- a
Answer: c
16) There are two families A and B. There are 4 men, 6 women and 2 children in family A and 2 men, 2 women and 4 children in family B. The Recommended daily allowance for calories is, man : 2400, women : 1900, Children : 1800 and for proteins is, man : 55, women : 45 and Child : 33
- b
- c
- a
- d
Answer: c
17) Use matrix multiplication to divide $30, 000 in two parts such that the total annual interest at 9% on the first part and 11% on the second part amounts to $3060
- 12000 and 18000
- 15000 and 15000
- 6000 and 24000
- 16000 and 12000
Answer: 12000 and 18000
18) Find x such that (xI + yA)² = A
- -y
- ±y
- 1
- y
Answer: ±y
19) Find the values of θ
- 2π
- π
- 3π
- -π
Answer: -π
20) Find AB
- d
- c
- b
- a
Answer: d
21) Find AB
- d
- b
- c
- a
Answer: a
22) Using the equation system
6x₁ + 3x₂ + 1x₃ = 22
6x₁ + 4x₂ - 2x₃ = 12
4x₁ - 3x₂ + 5x₃ = 10. Find x₁, x₂, x₃
- a
- c
- d
- b
Answer: a
23) Find the inverse of
- d
- a
- c
- b
Answer: c
24) Find SA
- b
- a
- c
- d
Answer: d
25) We can say A is
- Non - Convertible
- None of these
- Singular
- Non - Singular
Answer: Non - Singular
26) We can say A is
- Non - convertible
- None of these
- Singular
- Non - Singular
Answer: Non - Singular
27) The determinant of the transpose A′ is the same as
- The determinant of A'
- None of these
- The determinant of A
- The transpose A
Answer: The determinant of A
28) Interchange of any two rows (or any two) columns will
- Determinant becomes zero
- Change the algebraic sign of the determinant
- Not change the algebraic sign of the determinant
- None of these
Answer: Change the algebraic sign of the determinant
29) Multiplication of any one row (or one column) by a scalar k will
- Change the value of the determinant k-fold
- Matrix will diminish
- None of these
- Not change the value of the determinant k - fold
Answer: Change the value of the determinant k-fold
30) The addition of a multiple of any row (column) to another row (column) will leave
- The value of the determinant becomes 1
- None of these
- The value of the determinant unchanged
- The value of the determinant changes
Answer: The value of the determinant unchanged