RBSE Class 12 Maths Solutions Chapter 3 Matrices Ex 3.4

RBSE Class 12 Maths Solutions Chapter 3 Matrices Ex 3.4

Question 1.

$\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$
Answer:

Question 2.
$\left[\begin{array}{cc}2& 1\\ 1& 1\end{array}\right]$
Answer:

Question 3.
$\left[\begin{array}{cc}1& 3\\ 2& 7\end{array}\right]$
Answer:
Let A = $\left[\begin{array}{cc}1& 3\\ 2& 7\end{array}\right]$
For elementary operations
A = IA

Question 4.
$\left[\begin{array}{cc}2& 3\\ 5& 7\end{array}\right]$
Answer:
Let A = $\left[\begin{array}{cc}2& 3\\ 5& 7\end{array}\right]$
For elementary operations
A = IA

Question 5.
$\left[\begin{array}{cc}2& 1\\ 7& 4\end{array}\right]$
Answer:
Let A = $\left[\begin{array}{cc}2& 1\\ 7& 4\end{array}\right]$
For elementary operations
A = IA

Question 6.
$\left[\begin{array}{cc}2& 5\\ 1& 3\end{array}\right]$
Answer:
Let A = $\left[\begin{array}{cc}2& 5\\ 1& 3\end{array}\right]$
For elementary operations
A = IA

Question 7.
$\left[\begin{array}{cc}3& 1\\ 5& 2\end{array}\right]$
Answer:
Let A = $\left[\begin{array}{cc}3& 1\\ 5& 2\end{array}\right]$
For elementary operations
A = IA

Question 8.
$\left[\begin{array}{cc}4& 5\\ 3& 4\end{array}\right]$
Answer:
Let A = $\left[\begin{array}{cc}4& 5\\ 3& 4\end{array}\right]$
For elementary operations
A = IA

Question 9.
$\left[\begin{array}{cc}3& 10\\ 2& 7\end{array}\right]$
Answer:
Let A = $\left[\begin{array}{cc}3& 10\\ 2& 7\end{array}\right]$
For elementary operations
A = IA

Question 10.
$\left[\begin{array}{cc}3& -1\\ -4& 2\end{array}\right]$
Answer:
Let A = $\left[\begin{array}{cc}3& -1\\ -4& 2\end{array}\right]$
For elementary operations
A = IA

Question 11.
$\left[\begin{array}{cc}2& -6\\ 1& -2\end{array}\right]$
Answer:
Let A = $\left[\begin{array}{cc}2& -6\\ 1& -2\end{array}\right]$
For elementary operations
A = IA

Question 12.
$\left[\begin{array}{cc}6& -3\\ -2& 1\end{array}\right]$
Answer:
Let A = $\left[\begin{array}{cc}6& -3\\ -2& 1\end{array}\right]$
For elementary operations
A = IA

All the elements of second row are zero.
Thus, A-1 does not exists.

Question 13.
$\left[\begin{array}{cc}2& -3\\ -1& 2\end{array}\right]$
Answer:
Let A = $\left[\begin{array}{cc}2& -3\\ -1& 2\end{array}\right]$
For elementary operations

Question 14.
$\left[\begin{array}{cc}2& 1\\ 4& 2\end{array}\right]$
Answer:
Let A = $\left[\begin{array}{cc}2& 1\\ 4& 2\end{array}\right]$
For elementary operations
A = IA

All the elements of first row of left matrix are zero. Thus A-1 does not exist i.e., inverse of A does not exists.

Question 15.
$\left[\begin{array}{ccc}2& -3& 3\\ 2& 2& 3\\ 3& -2& 2\end{array}\right]$
Answer:

Question 16.
$\left[\begin{array}{ccc}1& 3& -2\\ -3& 0& -5\\ 2& 5& 0\end{array}\right]$
Answer:

Question 17.
$\left[\begin{array}{ccc}2& 0& -1\\ 5& 1& 0\\ 0& 1& 3\end{array}\right]$
Answer:

Question 18.
Matrices A and B will be inverse of each other if
(A) AB = BA
(B) AB = BA = 0
(C) AB = 0, BA = I
(D) AB = BA = I
Answer:
AB = BA = I, then A and B will be inversible to each other.
Hence, option (D) is correct.

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