Let = (1001) ( 1 0 0 1 ) p = (2345) ( 2 3 4 5 ) Q... | JAMB UTME - Mathematics - 1998

Question 1 Report

Let = $(\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix})$ p = $(\begin{matrix} 2 & 3 \\ 4 & 5 \end{matrix})$ Q = $(\begin{matrix} u & 4 + u \\ - 2 v & v \end{matrix})$ 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)

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Let = (1001) ( 1 0 0 1 ) p = (2345) ( 2 3 4 5 ) Q = (u4+u−2vv) ( u 4 + u − 2 v v ) be 2 x 2 matrices such that PQ = 1. Find (u, v)

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Let = (1001) ( 1 0 0 1 ) p = (2345) ( 2 3 4 5 ) Q = (u4+u−2vv) ( u 4 + u − 2 v v ) be 2 x 2 matrices such that PQ = 1. Find (u, v)

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