# GATE2015-3-15

The lowest eigenvalue of the $2\times 2$ matrix $\begin{bmatrix} 4 & 2\\ 1 & 3 \end{bmatrix}$ is ________

recategorized

## Related questions

For a given matrix $P=\begin{bmatrix} 4+3i & -i\\ i & 4-3i \end{bmatrix}$, where $i=\sqrt{-1}$, the inverse of matrix $P$ is $P=\displaystyle{\frac{1}{24}}\begin{bmatrix} 4-3i & i\\ -i & 4+3i \end{bmatrix} \\$ ... $P=\displaystyle{\frac{1}{25}}\begin{bmatrix} 4+3i & -i\\ i & 4-3i \end{bmatrix} \\$
The determinant of a $2 \times 2$ matrix is $50$. If one eigenvalue of the matrix is $10$, the other eigenvalue is _________.
If $A=\begin{bmatrix}1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 1 \end{bmatrix}$ then $\text{det}(A^{-1})$ is _______ (correct to two decimal palces).
If any two columns of a determinant $P=\begin{bmatrix} 4 & 7 & 8\\ 3 & 1 & 5\\ 9 & 6 & 2 \end{bmatrix}$ are interchanged, which one of the following statements regarding the value of the determinant is CORRECT? Absolute value remains unchanged ... . Both absolute value and sign will change. Absolute value will change but sign will not change. Both absolute value and sign will remain unchanged.