(1) By R1→R1+R2, \(\begin{bmatrix}0 &1\\1 &-1\end{bmatrix}\) is possible
(2) By R1↔R2, \(\begin{bmatrix}1&-1\\-1&2\end{bmatrix}\) is possible
(3) This matrix can’t be obtained
(4) By R2→R2+2R1, \(\begin{bmatrix}-1&2\\-1&3\end{bmatrix}\)is possible
So, the correct option is (C): \(\begin{bmatrix}-1&2\\-2&7\end{bmatrix}\)
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.