Test Index

CBSE Class 12 Maths 2010 Solved Paper

© examsnet.com
Question : 10 of 29
Marks: +1, -0
If [1234][3125]\left[ \begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array} \right] \left[ \begin{array}{cc} 3 & 1 \\ 2 & 5 \end{array} \right] = [711k23]\left[ \begin{array}{cc} 7 & 11 \\ k & 23 \end{array} \right] , then write the value of k.
Solution:  
Given [1234][3125]\left[ \begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array} \right] \left[ \begin{array}{cc} 3 & 1 \\ 2 & 5 \end{array} \right] = [711k23]\left[ \begin{array}{cc} 7 & 11 \\ k & 23 \end{array} \right]
Now using matrix multiplication in LHS, we get
[1×3+2×21×1+2×53×3+4×23×1+4×5]\left[ \begin{array}{cc} 1\times 3+2\times 2 & 1\times 1+2\times 5 \\ 3\times 3+4\times 2 & 3\times 1+4\times 5 \end{array} \right]
= [711k23]\left[ \begin{array}{cc} 7 & 11 \\ k & 23 \end{array} \right]
⇒ [3+41+109+83+20]\left[ \begin{array}{cc} 3+4 & 1+10 \\ 9+8 & 3+20 \end{array} \right] = [711k23]\left[ \begin{array}{cc} 7 & 11 \\ k & 23 \end{array} \right]
⇒ [7111723]\left[ \begin{array}{cc} 7 & 11 \\ 17 & 23 \end{array} \right] = [711k23]\left[ \begin{array}{cc} 7 & 11 \\ k & 23 \end{array} \right]
Now on equating the corresponding elements we get the value of k = 17
© examsnet.com
Go to Question:
Prev Question
Next Question