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 \e...

Assessment: JAMB UTME - Mathematics - 1998 Subject: General Mathematics

Question 1 Report

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}

)

Answer Details

PQ =

(\begin{matrix} 2 & 3 \\ 4 & 5 \end{matrix})

(\begin{matrix} u & 4 + u \\ - 2 v & v \end{matrix})

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

(\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix})

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{4u - 12v = 0}{-4u - 10v = 0}

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

\frac{5}{2}

∴ (U, V) = (-

\frac{5}{2}

- 1)

View Answer

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 \e...

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