Evaluate the determinant: \(\begin{vmatrix} 1 & 2 & 3 \\ -2 & -1 & -2 \\ 3 & 1 & 4 \end{vmatrix}\) [cite: 1]
A4
B2
C5
D0
Mathematics · Question Bank
Advanced Engineering Mathematics
64 questions · page 3 of 4. Answer in your head first, then check the solution.
Evaluate the determinant: \(\begin{vmatrix} 1 & 6 & 0 \\ 4 & 2 & 7 \\ 0 & 5 & 3 \end{vmatrix}\) [cite: 1]
A110
B-101
C101
D-110
Evaluate the determinant: \(\begin{vmatrix} 2 & 14 & 3 & 1 \\ 1 & 5 & -1 & 3 \\ 1 & -2 & 2 & -3 \\ 3 & -4 & -3 & -4 \end{vmatrix}\) [cite: 1]
A489
B389
C326
D452
Compute the value of x by determinant: \(x = \begin{vmatrix} 4 & -1 & 2 & 3 \\ 2 & 0 & 2 & 1 \\ 10 & 3 & 0 & 1 \\ 14 & 2 & 4 & 5 \end{vmatrix}\) [cite: 1]
A-32
B-28
C16
D52
Given the equations:
\(x+y+z=2\)
\(3x-y-2z=4\)
\(5x-2y+3z=-7\)
Solve for y by determinants. [cite: 1]
\(x+y+z=2\)
\(3x-y-2z=4\)
\(5x-2y+3z=-7\)
Solve for y by determinants. [cite: 1]
A1
B-2
C3
D0
Solve the equations by Cramer's Rule:
\(2x-y+3z=-3\)
\(3x+3y-z=10\)
\(-x-y+z=-4\) [cite: 1]
\(2x-y+3z=-3\)
\(3x+3y-z=10\)
\(-x-y+z=-4\) [cite: 1]
A(2, 1, -1)
B(2, -1, -1)
C(1, 2, -1)
D(-1, -2, 1)
If \(A = \begin{vmatrix} 2 & 3 & 1 \\ -1 & 2 & 4 \\ 0 & 5 & 7 \end{vmatrix}\), what is the cofactor of the second row, third column element? [cite: 1]
A\(\begin{vmatrix} 2 & 3 \\ 0 & 5 \end{vmatrix}\)
B-\(\begin{vmatrix} 2 & 3 \\ 0 & 5 \end{vmatrix}\)
C-\(\begin{vmatrix} 1 & 7 \\ 2 & 0 \end{vmatrix}\)
D\(\begin{vmatrix} 3 & 1 \\ 5 & 7 \end{vmatrix}\)
If \(A = \begin{vmatrix} 3 & 1 & 2 \\ -2 & -1 & 0 \\ 0 & 2 & -1 \end{vmatrix}\), what is the cofactor of the first row, second column element? [cite: 101]
A-\(\begin{vmatrix} 3 & 2 \\ 0 & -1 \end{vmatrix}\)
B\(\begin{vmatrix} -2 & -1 \\ 0 & 2 \end{vmatrix}\)
C\(\begin{vmatrix} 3 & 2 \\ 0 & -1 \end{vmatrix}\)
D-\(\begin{vmatrix} -2 & 0 \\ 0 & -1 \end{vmatrix}\)
If a \(3 \times 3\) matrix and its inverse are multiplied together, write the product. [cite: 101]
A\(\begin{vmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{vmatrix}\)
B\(\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}\)
C\(\begin{vmatrix} 0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0 \end{vmatrix}\)
D\(\begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}\)
If matrix \(\begin{bmatrix} 1 & -1 & 2 \\ 2 & 1 & 3 \\ 0 & -1 & 1 \end{bmatrix}\) is multiplied by \(\begin{bmatrix} x \\ y \\ z \end{bmatrix}\) is equal to zero, then matrix \(\begin{bmatrix} x \\ y \\ z \end{bmatrix}\) is [cite: 101]
A3
B1
C0
D-2
Given the matrix equation, solve for x and y:
\(\begin{bmatrix} 1 & 1 \\ 3 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 0 \end{bmatrix}\) [cite: 101]
\(\begin{bmatrix} 1 & 1 \\ 3 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 0 \end{bmatrix}\) [cite: 101]
A-4, 6
B-4, 2
C-4, -2
D-4, -6
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 [cite: 101]
A8
B1
C4
D0
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? [cite: 101]
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: \(\begin{bmatrix} 2 & 1 \\ -1 & 3 \end{bmatrix} + 2 \begin{bmatrix} -1 & 2 \\ 1 & 1 \end{bmatrix}\) [cite: 101]
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. [cite: 101]
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 \(\begin{bmatrix} 3 & 1 & 2 \\ -2 & -1 & 0 \\ 0 & 2 & -1 \end{bmatrix}\) [cite: 101]
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 \(\begin{bmatrix} 1 & 2 \\ 5 & 9 \end{bmatrix}\) [cite: 101]
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: [cite: 101]
A\(\cos kt\)
B\(\sin kt\)
C\(e^{kt}\)
D1.0
The Laplace transform of \(\cos \omega t\) is [cite: 101]
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 \(\frac{2}{s+1} - \frac{4}{s+3}\) [cite: 101]
A\(2e^{-t} - 4e^{-3t}\)
B\(e^{-2t} + e^{-3t}\)
C\(e^{-2t} - e^{-3t}\)
D\(2e^{-t}(1 - 2e^{-3t})\)