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If [latex]x\begin{bmatrix} -3\\ 4 \end{bmatrix}+y\begin{bmatrix} 4\\ 3 \end{bmatrix}=\begin{bmatrix} 10\\ -5 \end{bmatrix}[/latex], then

1) x = – 2, y = 1 2) x = – 9, y = 10 3) x = 22,... View Article

If A = [latex]\begin{bmatrix} 1 &-5 &7 \\ 0&7 &9 \\ 11&8 &9 \end{bmatrix}[/latex] then trace of the matrix is

1) 17 2) 25 3) 3 4) 12 Solution: (1) 17 \(\begin{array}{l}\begin{array}{l} A=\left[\begin{array}{ccc} 1 & -5 & 7 \\ 0... View Article

If A is a symmetric matrix and n ϵ N, then Aⁿ is

1) symmetric matrix 2) a diagonal matrix 3) a skew-symmetric 4) None of the above Solution: (1) symmetric matrix AT... View Article

If A = [latex]\begin{bmatrix} 2 &-1 \\ -1&2 \end{bmatrix}[/latex] and I is the unit matrix of order 2, then A² equals

1) 4A – 3I 2) 3A – 4I 3) A – I 4) A + I Solution: (1) 4A –... View Article

If A is square matrix A’ is its transpose, then 1/2(A – A’) is

1) a symmetric matrix 2) a skew – symmertic matrix 3) a unit matrix 4) an elementary matrix Solution: (2)... View Article

If o(A) = 2 × 3 , o(B) = 3 × 2 and o(C) = 3 × 3 , then which one of the following is not defined?

1) CB + A’ 2) BAC 3) C(A + B’)’ 4) C(A + B’ ) Solution: (4) C(A + B’... View Article

If [latex]\begin{bmatrix} 1 &x &1 \end{bmatrix}\begin{bmatrix} 1 &2 &3 \\ 0&5 &1 \\ 0&3 &2 \end{bmatrix}\begin{bmatrix} x\\ 1\\ -2 \end{bmatrix}[/latex]=0, then the value of x is

1) 0 2) 2/3 3) 5/4 4) – (4/5) Solution: (3) 5/4 \(\begin{array}{l}\begin{aligned} &\left[\begin{array}{lll} 1 & x & 1 \end{array}\right]\left[\begin{array}{lll}... View Article

The number of values of k for which the system of equations (k + 1)x + 8y = 4k; kx + (k + 3) y = 3k – 1 has infinitely many solutions is

1) 0 2) 1 3) 2 4) infinite Solution: (2) 1 For infinitely many solutions, (k + 1) / k... View Article

If A = [latex]\begin{bmatrix} 1 &2 &2 \\ 2&1 &2 \\ 2&2 &1 \end{bmatrix}[/latex] then A² – 4A =

1) 2I3 2) 3I3 3) 4I3 4) 5I3 Solution: (4) 5I3 \(\begin{array}{l}\begin{array}{l} A=\left[\begin{array}{lll} 1 & 2 & 2 \\ 2... View Article

If E (θ) = [latex]\begin{bmatrix} cos^{2}\theta &cos\theta sin\theta \\ cos\theta sin\theta& sin^{2}\theta \end{bmatrix}[/latex] and θ and ɸ differ by and odd multiple of π / 2, then E (θ) E (ɸ) is a

1) unit matrix 2) null matrix 3) diagonal matrix 4) None of these Solution: (2) null matrix \(\begin{array}{l}\begin{array}{l}E(\theta)=\left[\begin{array}{cc}\cos ^{2} \theta... View Article

If A = [latex]\begin{bmatrix} 0 &a \\ b&0 \end{bmatrix}^{4}=I[/latex], then

1) a = 1 = 2b 2) a = b 3) a = b2 4) ab = 1 Solution: (4)... View Article

If A = [latex]\begin{bmatrix} 1 &-2 \\ 4&5 \end{bmatrix}[/latex] and f (t) = t² – 3t + 7, then f (A) + [latex]\begin{bmatrix} 3 &6 \\ -12&9 \end{bmatrix}[/latex] =

1) \(\begin{array}{l}\begin{bmatrix} 1 &0 \\ 0&1 \end{bmatrix}\end{array} \) 2) \(\begin{array}{l}\begin{bmatrix} 0 &0 \\ 0&0 \end{bmatrix}\end{array} \) 3) \(\begin{array}{l}\begin{bmatrix} 0 &1... View Article

If ω is a complex cube root of unity and if 1, ω and ω² are the cube roots of unity and [latex]begin{bmatrix} omega &0 \ 0&omega end{bmatrix}[/latex], then A⁵⁰ =

1) ω2 A 2) ωA 3) A 4) 0 Solution: (2) ωA \(\begin{array}{l}\begin{array}{l} A=\left[\begin{array}{cc} w & 0 \\ 0 &... View Article

If A and B are two symmetric matrices of the same order. Then, the matrix AB – BA is equal to

1) a symmetric matrix 2) a skew-symmetric matrix 3) a null matrix 4) the identity matrix Solution: (2) a skew-symmetric... View Article

If A is a square matrix, then

1) A + AT is symmetric 2) AAT is skew-symmetric 3) AT + A is skew-symmetric 4) AT is skew-symmetric... View Article

Let 𝞈 = (- 1 / 2) + i (√3 / 2), then the value of the determinant [latex]\begin{vmatrix} 1 &1 &1 \\ 1&-1-\omega^{2} &\omega^{2} \\ 1& \omega^{2} & \omega \end{vmatrix}[/latex] is

1) 3ω 2) 3ω (ω – 1) 3) 3ω2 4) 3ω (1 – ω) Solution: (2) 3ω (ω – 1)... View Article

If [latex]A=\begin{bmatrix} x &1 \\ 1&0 \end{bmatrix}[/latex] and A² is the identity matrix, then x =

1) –1 2) 0 3) 1 4) 2 Solution: (2) 0 \(\begin{array}{l}\begin{array}{l} A=\left[\begin{array}{ll} x & 1 \\ 1 & 0... View Article

If A^T and B^T are transpose matrices of the square matrices A and B respectively then (AB)^T is equal to

1) AT BT 2) ABT 3) BAT 4) BT AT Solution: (4) BT AT AT and BT are transpose matrices... View Article

If A = [aij]_2×2, where a_ij = i + j, then A is equal to

1) \(\begin{array}{l}\begin{bmatrix} 1 &1 \\ 2&2 \end{bmatrix}\end{array} \) 2) \(\begin{array}{l}\begin{bmatrix} 1 &2 \\ 1&2 \end{bmatrix}\end{array} \) 3) \(\begin{array}{l}\begin{bmatrix} 1 &2... View Article

If the matrices [latex]A=\begin{bmatrix} 2 &1 &3 \\ 4&1 &0 \end{bmatrix},B=\begin{bmatrix} 1 &-1 \\ 0&2 \\ 5&0 \end{bmatrix}[/latex] then AB will be

1) \(\begin{array}{l}\begin{bmatrix} 17 &0 \\ 4&-2 \end{bmatrix}\end{array} \) 2) \(\begin{array}{l}\begin{bmatrix} 4 &0 \\ 0&4 \end{bmatrix}\end{array} \) 3) \(\begin{array}{l}\begin{bmatrix} 17 &4... View Article

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