\(\begin{pmatrix} -8 & -5 \\ 3 & 2 \end{pmatrix}\)
\(\begin{pmatrix} -8 & -5 \\ 3 & -2 \end{pmatrix}\)
\(\begin{pmatrix} -8 & -5 \\ -3 & 2 \end{pmatrix}\)
\(\begin{pmatrix} -8 & -5 \\ -3 & -2 \end{pmatrix}\)
Correct answer is A
Let \(\begin{pmatrix} a & b \\ c & d \end{pmatrix} = T^{-1}\)
\(T . T^{-1} = I\)
\(\begin{pmatrix} -2 & -5 \\ 3 & 8 \end{pmatrix}\begin{pmatrix} a & b \\ c & d \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\)
\(\implies -2a - 5c = 1\)
\(-2b - 5d = 0 \implies b = \frac{-5d}{2}\)
\(3a + 8c = 0 \implies a = \frac{-8c}{3}\)
\(3b + 8d = 1\)
\(-2(\frac{-8c}{3}) - 5c = \frac{16c}{3} - 5c = \frac{c}{3} = 1 \implies c = 3\)
\(3(\frac{-5d}{2}) + 8d = \frac{-15d}{2} + 8d = \frac{d}{2} = 1 \implies d = 2\)
\(b = \frac{-5 \times 2}{2} = -5\)
\(a = \frac{-8 \times 3}{3} = -8\)
\(\therefore T^{-1} = \begin{pmatrix} -8 & -5 \\ 3 & 2 \end{pmatrix}\)
Find the coordinates of the centre of the circle \(3x^{2}+3y^{2} - 4x + 8y -2=0\)...
Rationalize; \(\frac{1}{\sqrt{2 + 1}}\)...
The marks scored by 4 students in Mathematics and Physics are ranked as shown in the table below ...
The table shows the distribution of marks obtained by some students in a test Marks 0-9 10-...
If \(\begin{vmatrix} 1+2x & -1 \\ 6 & 3-x \end{vmatrix} = -3 \), find the values of x....
Express the force F = (8 N, 150°) in the form (a i + b j) where a and b are constants ...
If α and β are roots of x\(^2\) + mx - n = 0, where m and n are constants, form the ...