\(A = \begin{pmatrix} -3 & -5 \\ 1 & 2 \end{pmatrix}\)
\(A = \begin{pmatrix} 3 & -5 \\ 1 & 2 \end{pmatrix}\)
\(A = \begin{pmatrix} 3 & -5 \\ -1 & 2 \end{pmatrix}\)
\(A = \begin{pmatrix} -3 & 5 \\ 1 & -2 \end{pmatrix}\)
Correct answer is C
\(B.B^{-1} = 1\), let \(B^{-1} = \begin{pmatrix} a & b \\ c & d \end{pmatrix}\)
\(\begin{pmatrix} 2 & 5 \\ 1 & 3 \end{pmatrix}\)\(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\) = \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\)
Multiplying \(B \times B^{-1}\), we have the following equations:
\(2a+5c = 1......... (1)\); \(a+3c = 0 ........(2)\)
\(2b+5d = 0 ..........(3)\); \(b+3d = 1..........(4)\)
Solving the equations simultaneously, we have
\(a = 3; b = -5; c = -1; d = 2 \implies B^{-1} = \begin{pmatrix} 3 & -5 \\ -1 & 2 \end{pmatrix}\)
Resolve \(\frac{3x - 1}{(x - 2)^{2}}, x \neq 2\) into partial fractions....
A force 10N acts in the direction 060° and another force 6N acts in the direction 330°. Find...
Given that \(\frac{3x + 4}{(x - 2)(x + 3)}≡\frac{P}{x + 3}+\frac{Q}{x - 2}\),find the value of...
A stone is thrown vertically upward and distance, S metres after t seconds is given by S = 12t ...
If \(\frac{6x + k}{2x^2 + 7x - 15}\) = \(\frac{4}{x + 5} - \frac{2}{2x - 3}\). Find the value ...
Evaluate \(\frac{1}{1 - \sin 60°}\), leaving your answer in surd form....