MATRICES

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Question: The number of solutions of the system of equations: 2x + y − z = 7 x − 3y + 2z = 1 x + 4y − 3z = 5 (a) 3 (b) 2 (c) 1 (d) 0
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Question: The system of linear equations \[ x + y + z = 2, \] \[ 2x = y - z = 3, \] \[ 3x + 2y + kz = 4 \] has a unique solution if (A) \( k \neq 0
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Question: Solve the following system of homogeneous linear equations by matrix method: x + y + z = 0, x - y - 5z = 0, x + 2y + 4z = 0
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129
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Question: If each element of a 3×3 matrix is multiplied by 3, then the determinant of the newly formed matrix is Options: A: 3|A| B: 9|A| C: 27|A| D:
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60
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Question: If A and B are square matrices of order 3 such that |A| = −1, |B| = 3, then the determinant of 3AB is equal to Options: A: −9 B: −27 C: −81
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103
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Question: From the matrix equation AB=AC we can conclude B=C provided the matrix A is Options: A: singular B: non singular C: symmetric D: None of th
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81
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Question: If A = [-1 -2 2 2 1 -2 2 -2 1] the adj. A = Options: A: A B: A T C: 3 A D: 3 A T
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61
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Question: If A = ⎡⎢⎣ 0 −1 −4 1 0 −7 4 7 0 ⎤⎥⎦ then AT = Options: A: O B: I C: A D: −A
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55
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Question: If A and B are symmetric matrices of the same order, then AB - BA is a matrix which is Options: A: null B: unit C: symmetric D: skew symmet
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128
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Question: If A = [a b b 2−a 2−a b] then A is Options: A: Idempotent B: Involutary C: Nilpotent D: Scalar
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103
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Question: If (123)A = (45), what is the order of matrix A? Options: A: 3 × 2 B: 3 × 1 C: 2 × 3 D: 2 × 1
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102
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Question: The inverse of the matrix \( A = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix} \) is equal to Options: A: A B: A' C: \(
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143
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Question: Let A be a 2×2 matrix. Statement 1: adj(adj A) = A. Statement 2: |adj A| = |A|. Which statement is true? Options: A: Statement 1 is right B
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214
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Question: If A is a singular matrix then Adj is Options: A: non singular B: singular C: symmetric D: skew symmetric
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88
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Question: If A = [cosθ sinθ −sinθ cosθ] and A(adjA) = λI then λ is equal to Options: A: 1 B: 2 C: 3 D: sinθcosθ
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68
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Question: For a 3×3 matrix A, if det A = 4, then det (Adj. A) equals Options: A: −4 B: 4 C: 16 D: 64
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74
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Question: If A = ⎡⎢⎣ 1 0 0 0 1 0 a b −1 ⎤⎥⎦ then A² is equal to Options: A: A B: −A C: Null matrix D: I
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60
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Question: If A = [1 2 3 4], B = [a 0 0 b] where a, b ∈ N. If AB = BA then there exists Options: A: only one B B: infinitely many B's C: more than one
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66
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Question: If A = [α 0 1 1], B = [1 0 5 1] whenever A^2 = B then the value of α is Options: A: 1 B: −1 C: 4 D: no real value of α
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141
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Question: If A = [i 0 0 i] then A^2 = Options: A: [1 0 0 -1] B: [-1 0 0 -1] C: [1 0 0 1] D: [-1 0 0 1]
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113
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