Matrices P and Q satisfies PQ - Q -1- where Q -2-120- Find the value of K for which KP -2 Q -1- I -0-A- 4B- 6C- 3D- 2

The correct option is D 2PQ=Q 1 nbsp;orPQ2=Ipost multiplying nbsp;both nbsp;side nbsp;by nbsp;QNow,KP 2Q 1+I=0or nbsp;KPQ 2Q 1Q+IQ=0post multiplyin ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Multiplying/Dividing a Positive Entity

Matrices P an...

Question

Matrices P and Q satisfies $PQ = Q^{- 1}$ , where $Q = (\begin{matrix} 2 & - 1 2 & 0 \end{matrix}]$ . Find the value of K for which $KP - 2 Q^{- 1} + I = 0 .$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A 2
$PQ = Q^{- 1} or {PQ}^{2} = I (post - multiplying both side by Q) Now, KP - 2 Q^{- 1} + I = 0 or KPQ - 2 Q^{- 1} Q + IQ = 0 (post - multiplying both side by Q) \Rightarrow KPQ - 2 I + Q = 0 \Rightarrow {KPQ}^{2} - 2 Q + Q^{2} = 0 \Rightarrow KI - 2 Q + Q^{2} = 0 now, by putting the value of Q and I, we get - K (\begin{matrix} 1 & 0 0 & 1 \end{matrix}] - 2 (\begin{matrix} 2 & - 1 2 & 0 \end{matrix}] + (\begin{matrix} 2 & - 1 2 & 0 \end{matrix}] (\begin{matrix} 2 & - 1 2 & 0 \end{matrix}] = (\begin{matrix} 0 & 0 0 & 0 \end{matrix}] \Rightarrow (\begin{matrix} K & 0 0 & K \end{matrix}] - (\begin{matrix} 4 & - 2 4 & 0 \end{matrix}] + (\begin{matrix} 2 & - 2 4 & - 2 \end{matrix}] = (\begin{matrix} 0 & 0 0 & 0 \end{matrix}] \Rightarrow (\begin{matrix} K - 2 & 0 0 & K - 2 \end{matrix}] = (\begin{matrix} 0 & 0 0 & 0 \end{matrix}] \Rightarrow K = 2$

Suggest Corrections

Similar questions

Q. Matrices P and Q satisfies

PQ = Q^{- 1}

, where

Q = (\begin{matrix} 2 & - 1 2 & 0 \end{matrix}]

. Find the value of K for which

KP - 2 Q^{- 1} + I = 0 .

Q. Let

P

and

Q

be 2*2 matrices. Consider the statements.

P Q = 0 \Rightarrow 1) P = 0

Q = 0

b o t h

P Q = I_{2} \Rightarrow P = Q^{- 1}

(P + Q)^{2} = P^{2} + 2 P Q + Q^{2}

Q. Let P and Q be two

2 \times 2

matrices. Consider the statements i)

P Q = O \Rightarrow P = O

Q = O

or both
ii)

P Q = I_{2} \Rightarrow P = Q^{- 1}

iii)

{(P + Q)}^{2} = P^{2} + 2 P Q + Q^{2}

. Then

The numbers P, Q and R for which the function
$f (x) = P e^{2 x} + Q e^{x} + R x$ satisfies the conditions
$f (0) = - 1, f^{^{'}} (l o g 2) = 31$ and $\int_{0}^{l o g 4} [f (x) - R x] d x = \frac{39}{2}$ are
given by

Q. If

p

and

q

are prime numbers satisfying the condition

p^{2} - 2 q^{2} = 1

, then the value of

p^{2} + 2 q^{2}

Join BYJU'S Learning Program

Matrices P and Q satisfies PQ=Q−1, where Q=(2−120]. Find the value of K for which KP−2Q−1+I=0.

Matrices P and Q satisfies $PQ = Q^{- 1}$ , where $Q = (\begin{matrix} 2 & - 1 2 & 0 \end{matrix}]$ . Find the value of K for which $KP - 2 Q^{- 1} + I = 0 .$