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If U = [latex]\begin{bmatrix} 2 &-3 &4 \end{bmatrix},X=\begin{bmatrix} 0 &2 &3 \end{bmatrix},V=\begin{bmatrix} 3\\ 2\\ 1 \end{bmatrix},Y=\begin{bmatrix} 2\\ 2\\ 4 \end{bmatrix}[/latex], then UV + XY =

1) [20] 2) 20 3) [-20] 4) - 20 Solution: (1) [20]... View Article

If A = [latex]\begin{bmatrix} 1 &1 \\ 1&1 \end{bmatrix}[/latex] then A¹⁰⁰ =

1) 2100A 2) 299A 3) 100A 4) 299A Solution: (2) 299A... View Article

If matrix A = [latex]\begin{bmatrix} 1 &-3 \\ 2&k \end{bmatrix}[/latex] and A² – 4A + 10I = A, then k =

1) 0 2) - 4 3) 4 but not 1 4) 1 or 4 Solution: (3) 4 but not 1... View Article

If matrix A = [latex]\begin{bmatrix} 1/\sqrt{2} &1/\sqrt{2} \\ -1/\sqrt{2}& -1/\sqrt{2} \end{bmatrix}[/latex] is

If matrix A = is 1) unitary 2) orthogonal 3) nilpotent 4) involutary Solution: (3) nilpotent Matrix A is nilpotent of 2 x 2.... View Article

If A (ɑ) = [latex]\begin{bmatrix} cos\alpha &sin\alpha \\ -sin\alpha& cos\alpha \end{bmatrix}[/latex], then the matrix A² (ɑ) =

1) A(2α) 2) A(α) 3) A(3α) 4) A(4α) Solution: (1) A(2α)... View Article

If A = [latex]\begin{bmatrix} 1 &2 \\ 2&4 \end{bmatrix}[/latex] and B = [latex]\begin{bmatrix} a &0 \\ 0&b \end{bmatrix}[/latex] a, b ∈ N. Then,

1) there exist more than one but number of B's such that AB = BA 2) there exist exactly more B such that AB = BA 3) there exists infinitely... View Article

If A and B are square matrices of size n × n such that A² – B² = (A – B)(A + B), then which of the following will be always correct?

1) AB = BA 2) either A or B is a zero matrix 3) either A or B is an identity matrix 4) A = B Solution: (1) AB = BA A2 – B2 = (A – B)(A + B)... View Article

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, y = 1 4) x = 2, y = – 1 Solution: (1) x = – 2, y = 1 - 3x + 4y = 10 4x + 3y = - 5 - 3x +... 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... 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 = A [because A is... 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 – 3I... 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) a skew-symmetric matrix A is a... 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' ) O (A) = 2 x 3; O (B) = 3 x 2; O (C) = 3 x 3 O (A’) = 3 x 2; O (B’) =... View Article