If matrix \(\begin{bmatrix} 1 & 4 \\ -4 & 1 \end{bmatrix}\) is multiplied by \(\begin{bmatrix} x \\ y \end{bmatrix}\) is equal to zero, then matrix \(\begin{bmatrix} x \\ y \end{bmatrix}\) is
A8
B1
C4
D0
Mathematics · Question Bank
Advanced Engineering Mathematics
65 of 84 questions match · page 3 of 4. Answer in your head first, then check the solution.
If \(A = \begin{bmatrix} 4 & 5 & 0 \\ 6 & 7 & 3 \\ 1 & 2 & 5 \end{bmatrix}\) and \(B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\), what is A times B equal to?
A\(\begin{bmatrix} 4 & 0 & 0 \\ 0 & 7 & 0 \\ 0 & 0 & 5 \end{bmatrix}\)
B\(\begin{bmatrix} 0 & 0 & 0 \\ 0 & 7 & 0 \\ 1 & 0 & 0 \end{bmatrix}\)
C\(\begin{bmatrix} 6 & 7 & 0 \\ 8 & 9 & 4 \\ 2 & 3 & 5 \end{bmatrix}\)
D\(\begin{bmatrix} 4 & 5 & 0 \\ 6 & 7 & 3 \\ 1 & 2 & 5 \end{bmatrix}\)
Evaluate: \(\begin{bmatrix} 2 & 1 \\ -1 & 3 \end{bmatrix} + 2 \begin{bmatrix} -1 & 2 \\ 1 & 1 \end{bmatrix}\)
A\(\begin{bmatrix} -1 & 2 \\ 1 & 1 \end{bmatrix}\)
B\(\begin{bmatrix} 2 & 1 \\ -1 & 3 \end{bmatrix}\)
C\(\begin{bmatrix} -2 & 4 \\ 2 & 2 \end{bmatrix}\)
D\(\begin{bmatrix} 0 & 5 \\ 1 & 5 \end{bmatrix}\)
Elements of matrix \(B = \begin{bmatrix} 1 & 2 \\ 0 & -5 \end{bmatrix}\) and elements of matrix \(C = \begin{bmatrix} 3 & 6 \\ 4 & 1 \end{bmatrix}\). Find the elements of the product matrix BC.
A\(\begin{bmatrix} 11 & 8 \\ -20 & -5 \end{bmatrix}\)
B\(\begin{bmatrix} -11 & 8 \\ 19 & 5 \end{bmatrix}\)
C\(\begin{bmatrix} -10 & 9 \\ -19 & 6 \end{bmatrix}\)
D\(\begin{bmatrix} -11 & 9 \\ -20 & -4 \end{bmatrix}\)
Transpose the matrix \(\begin{bmatrix} 3 & 1 & 2 \\ -2 & -1 & 0 \\ 0 & 2 & -1 \end{bmatrix}\)
A\(\begin{bmatrix} -1 & 2 & 0 \\ 0 & -1 & -2 \\ 2 & 1 & 3 \end{bmatrix}\)
B\(\begin{bmatrix} 3 & -2 & 0 \\ 1 & -1 & 2 \\ 2 & 0 & -1 \end{bmatrix}\)
C\(\begin{bmatrix} 3 & 1 & 2 \\ 1 & 2 & -1 \\ -2 & -1 & 0 \end{bmatrix}\)
D\(\begin{bmatrix} 1 & 3 & 2 \\ -1 & -2 & 0 \\ 2 & 2 & -1 \end{bmatrix}\)
Determine the inverse matrix of \(\begin{bmatrix} 1 & 2 \\ 5 & 9 \end{bmatrix}\)
A\(\begin{bmatrix} -9 & 5 \\ 2 & -1 \end{bmatrix}\)
B\(\begin{bmatrix} 9 & 5 \\ 2 & 1 \end{bmatrix}\)
C\(\begin{bmatrix} 2 & 5 \\ 9 & 1 \end{bmatrix}\)
D\(\begin{bmatrix} -9 & -5 \\ 2 & 1 \end{bmatrix}\)
\(\frac{k}{s^2 + k^2}\) is the Laplace transform of:
A\(\cos kt\)
B\(\sin kt\)
C\(e^{kt}\)
D1.0
The Laplace transform of \(\cos \omega t\) is
A\(\frac{s}{s^2 + \omega^2}\)
B\(\frac{\omega}{s^2 + \omega^2}\)
C\(\frac{\omega}{s + \omega}\)
D\(\frac{s}{s + \omega}\)
Find the inverse Laplace transform of \(\frac{2}{s+1} - \frac{4}{s+3}\)
A\(2e^{-t} - 4e^{-3t}\)
B\(e^{-2t} + e^{-3t}\)
C\(e^{-2t} - e^{-3t}\)
D\(2e^{-t}(1 - 2e^{-3t})\)
The inverse Laplace transform of \(\frac{s}{s^2 + \omega^2}\) is
A\(\sin \omega t\)
B\(\omega\)
C\(e^{\omega t}\)
D\(\cos \omega t\)
Find the inverse Laplace transform of \(\frac{2s-18}{s^2+9}\) as a function of x.
A\(2 \cos x - \sin 3x\)
B\(2 \cos 3x - 6 \sin 3x\)
C\(3 \cos 2x - 2 \sin 6x\)
D\(6 \cos x - 3 \sin 2x\)
If \(z_1 = 1 - i\) and \(z_2 = -2 + 4i\), evaluate \(z_1^2 + 2z_1 - 3\).
A−1 + 4i
B1 − 4i
C−1 − 4i
D1 + 4i
Find the value of \(4\sinh\left(\dfrac{\pi i}{3}\right)\).
A\(2\sqrt{3}\,i\)
B\(4\sqrt{3}\,i\)
C\(\sqrt{3}\,i\)
D\(3\sqrt{3}\,i\)
Evaluate \((8 + 7i)^2\).
A15 + 112i
B15 − 112i
C−15 + 112i
D−15 − 112i
For a complex number \(z = 3 + j4\), the modulus is
A3
B4
C5
D6
Evaluate the inverse Laplace transform of \(\dfrac{6}{s^2 + 4}\).
A3 sin 2t
B3 cos 2t
C3 sinh 2t
D3 cosh 2t
Evaluate \(\mathcal{L}\{\sin t\cos t\}\).
A\(\dfrac{1}{2(s^2 + 4)}\)
B\(\dfrac{1}{s^2 + 4}\)
C\(\dfrac{1}{s^2 + 1}\)
D\(\dfrac{1}{2(s^2 + 1)}\)
Which one is not a fourth root of unity?
A1
B−1
Ci
D\(\dfrac{i}{\sqrt{2}}\)
If \(i = (-1)^{1/2}\), find the value of \(i^{36}\).
A−1
Bi
C−i
D1
For a complex number \(Z = 2 + 2\sqrt{3}\,i\), the modulus is
A2
B3
C4
D5