Home » Let = (begin{pmatrix} 1 & 0 \ 0 & 1 end{pmatrix}) p = (begin{pmatrix} 2…

Let = (begin{pmatrix} 1 & 0 \ 0 & 1 end{pmatrix}) p = (begin{pmatrix} 2…

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)
  • A.
    (-(frac{5}{2}) – 1)
  • B.
    (-(frac{5}{2}) – (frac{3}{2}))
  • C.
    (-(frac{5}{6}) – 1)
  • D.
    ((frac{5}{2}) – (frac{3}{2}))
Correct Answer: Option A
Explanation

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)

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