Question on: JAMB Mathematics - 1998

Let = (\begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}) p = (\begin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix}) Q = (\begin{pmatrix} u & 4+u \ -2v & v \end{pmatrix}) be 2 x 2 matrices such that PQ = 1. Find (u, v)

(-\(\frac{5}{2}\) - 1)

(-\(\frac{5}{2}\) - \(\frac{3}{2}\))

(-\(\frac{5}{6}\) - 1)

(\(\frac{5}{2}\) - \(\frac{3}{2}\))

Ask EduPadi AI for a detailed answer

Correct Option: A

PQ = (\begin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix})(\begin{pmatrix} u & 4+u \ -2v & v \end{pmatrix})

= (\begin{pmatrix} (2u-6v & 2(4+u) +3v)\ 4u-10v & 4(4+u)+5v \end{pmatrix})

= (\begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix})

2u - 6v = 1.....(i)

4u - 10v = 0.......(ii)

2(4 + u) + 3v = 0......(iii)

4(4 + u) + 5v = 1......(iv)

2u - 6v = 1 .....(i) x 2

4u - 10v = 0......(ii) x 1

(\frac{\text{4u - 12v = 0}}{\text{-4u - 10v = 0}})

-2v = 2 = v = -1

2u - 6(-1) = 1 = 2u = 5

u = -(\frac{5}{2})

∴ (U, V) = (-(\frac{5}{2}) - 1)