On using elementary column operations C 2 - 2 C 1 in the following matrix equation = , we have

On using elementary column operations C 2 - 2 C 1 in the fol — Class 12 Maths Solution

Matrices — Class 12 Maths Solution

exemplar objective MCQ NCERT,Exemp,Q.no.66,Page 61

Question

On using elementary column operations ${C_2} \to {C_2} - 2{C_1}$ in the following matrix equation $\left[ {\begin{array}{cccccccccccccccccccc}1&{ - 3}\\2&4\end{array}} \right] = \left[ {\begin{array}{cccccccccccccccccccc}1&{ - 1}\\0&1\end{array}} \right]\left[ {\begin{array}{cccccccccccccccccccc}3&1\\2&4\end{array}} \right]$, we have

(a) $\left[ {\begin{array}{cccccccccccccccccccc}1&{ - 5}\\0&4\end{array}} \right] = \left[ {\begin{array}{cccccccccccccccccccc}1&{ - 1}\\{ - 2}&2\end{array}} \right]\left[ {\begin{array}{cccccccccccccccccccc}3&{ - 5}\\2&0\end{array}} \right]$
(b) $\left[ {\begin{array}{cccccccccccccccccccc}1&{ - 5}\\0&4\end{array}} \right] = \left[ {\begin{array}{cccccccccccccccccccc}1&{ - 1}\\0&1\end{array}} \right]\left[ {\begin{array}{cccccccccccccccccccc}3&{ - 5}\\{ - 0}&2\end{array}} \right]$
(c) $\left[ {\begin{array}{cccccccccccccccccccc}1&{ - 5}\\2&0\end{array}} \right] = \left[ {\begin{array}{cccccccccccccccccccc}1&{ - 3}\\0&1\end{array}} \right]\left[ {\begin{array}{cccccccccccccccccccc}3&1\\{ - 2}&4\end{array}} \right]$
(d) $\left[ {\begin{array}{cccccccccccccccccccc}1&{ - 5}\\2&0\end{array}} \right] = \left[ {\begin{array}{cccccccccccccccccccc}1&{ - 1}\\0&1\end{array}} \right]\left[ {\begin{array}{cccccccccccccccccccc}3&{ - 5}\\2&0\end{array}} \right]$ ✓ Correct

Step-by-step Solution

Given that, $\left[ {\begin{array}{llllllllllllllllllll}1&{ - 3}\\2&4\end{array}} \right]$

$= \left[ {\begin{array}{cccccccccccccccccccc}1&{ - 1}\\0&1\end{array}} \right]\left[ {\begin{array}{llllllllllllllllllll}3&1\\2&4\end{array}} \right]$

On using ${C_2} \to {C_2} - 2{C_1},$ $\left[ {\begin{array}{cccccccccccccccccccc}1&{ - 5}\\2&0\end{array}} \right]$

$= \left[ {\begin{array}{cccccccccccccccccccc}1&{ - 1}\\0&1\end{array}} \right]\left[ {\begin{array}{cccccccccccccccccccc}3&{ - 5}\\2&0\end{array}} \right]$

Since, on using elementary column operation on $X = AB$,

we apply these operations simultaneously on $X$ and on the second matrix $B$ of the product $AB$ on RHS.

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Matrices. Curated by Sachin Sharma. Free for all students.