Let A be a 2 \times 2 symmetric matrix such that A\left[\begin{array}{c}1 \ 1]\end{array}=\left[\begin{array}{c}3 \ 7]\end{array} and the determinant of A be 1 . If A^{-1}=\alpha A+\beta I, where I is an identity matrix of order 2 \times 2, then \alpha+\beta equals ..... [4 Apr 2024 Shift 2]

Matrices and Determinants Part 3

Section: Mathematics

Question : 10 of 100

Marks: +1, -0

Let A be a 2×2 symmetric matrix such that A[

]=[

] and the determinant of A be 1 . If A−1=αA+βI, where I is an identity matrix of order 2×2, then α+β equals .....

[4 Apr 2024 Shift 2]

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α+β	2α
2α	5α+β

5	−2
−2	1

5	−2
−2	1