Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

If A = \(\begin{bmatrix}5 & 7\\4 & 6 \end{bmatrix}\), then what can be said about 14\( { A }^{ -1 } \)?

Options:

14\( { A }^{ -1 } \) = 7 (adj A)

14\( { A }^{ -1 } \) = -7 (adj A)

14\( { A }^{ -1 } \) = 14 (adj A)

14\( { A }^{ -1 } \) = -14 (adj A)

Correct Answer:

14\( { A }^{ -1 } \) = 7 (adj A)

Explanation:

\( { A }^{ -1 } \) =\(\frac{adj A}{|A|}\)

so, |A| = 2

So, \(14 { A }^{ -1 } \) =\(\frac{14×adj A}{2}\)

so, \(14{ A }^{ -1 } = 7 (adj A)\)