GATE 2018 EE – Question 27
Consider a non-singular $2\times2$ square matrix $\mathbf A$. If $\text{trace}(\mathbf A)=4$ and $\text{trace}(\mathbf A^2)=5$, the determinant of the matrix $\mathbf A$ is ________ (up to 1 decimal place).
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Correct answer: 5.47 to 5.53
Explanation
For eigenvalues $\lambda_1,\lambda_2$: $\lambda_1+\lambda_2=4$ and $\lambda_1^2+\lambda_2^2=5$. Then $2\lambda_1\lambda_2=16-5=11$, so $\det A=\lambda_1\lambda_2=5.5$.