Maharashtra Board 12th Commerce Maths Solutions Chapter 2 Matrices Ex 2.5

Balbharati Maharashtra State Board 12th Commerce Maths Solution Book Pdf Chapter 2 Matrices Ex 2.5 Questions and Answers.

Maharashtra State Board 12th Commerce Maths Solutions Chapter 2 Matrices Ex 2.5

Question 1.
Apply the given elementary transformation on each of the following matrices:
(i) \(\left[\begin{array}{cc}
3 & -4 \\
2 & 2
\end{array}\right]\), R₁ ↔ R₂
(ii) \(\left[\begin{array}{cc}
2 & 4 \\
1 & -5
\end{array}\right]\), C₁ ↔ C₂
(iii) \(\left[\begin{array}{ccc}
3 & 1 & -1 \\
1 & 3 & 1 \\
-1 & 1 & 3
\end{array}\right]\) 3R₂ and C₂ → C₂ – 4C₁
Solution:

Question 2.
Transform \(\left[\begin{array}{ccc}
1 & -1 & 2 \\
2 & 1 & 3 \\
3 & 2 & 4
\end{array}\right]\) into an upper triangularmatrix by suitable row transformations.
Solution:

Question 3.
Find the cofactor matrix of the following matrices:
(i) \(\left[\begin{array}{cc}
1 & 2 \\
5 & -8
\end{array}\right]\)
(ii) \(\left[\begin{array}{ccc}
5 & 8 & 7 \\
-1 & -2 & 1 \\
-2 & 1 & 1
\end{array}\right]\)
Solution:

Question 4.
Find the adjoint of the following matrices:
(i) \(\left[\begin{array}{cc}
2 & -3 \\
3 & 5
\end{array}\right]\)
(ii) \(\left[\begin{array}{ccc}
1 & -1 & 2 \\
-2 & 3 & 5 \\
-2 & 0 & -1
\end{array}\right]\)
Solution:

Question 5.
Find the inverses of the following matrices by the adjoint mathod:
(i) \(\left[\begin{array}{rr}
3 & -1 \\
2 & -1
\end{array}\right]\)
(ii) \(\left[\begin{array}{cc}
2 & -2 \\
4 & 5
\end{array}\right]\)
(iii) \(\left[\begin{array}{lll}
1 & 2 & 3 \\
0 & 2 & 4 \\
0 & 0 & 5
\end{array}\right]\)
Solution:

Question 6.
Find the inverses of the following matrices by the transformation method:
(i) \(\left[\begin{array}{cc}
1 & 2 \\
2 & -1
\end{array}\right]\)
(ii) \(\left[\begin{array}{ccc}
2 & 0 & -1 \\
5 & 1 & 0 \\
0 & 1 & 3
\end{array}\right]\)
Solution:

Question 7.
Find the inverse of A = \(\left[\begin{array}{lll}
1 & 0 & 1 \\
0 & 2 & 3 \\
1 & 2 & 1
\end{array}\right]\) by elementary column transformations.
Solution:

Question 8.
Find the inverse of \(\left[\begin{array}{lll}
1 & 2 & 3 \\
1 & 1 & 5 \\
2 & 4 & 7
\end{array}\right]\) by the elementary row transformations.
Solution:

Question 9.
If A = \(\left[\begin{array}{lll}
1 & 0 & 1 \\
0 & 2 & 3 \\
1 & 2 & 1
\end{array}\right]\) and B = \(\left[\begin{array}{lll}
1 & 2 & 3 \\
1 & 1 & 5 \\
2 & 4 & 7
\end{array}\right]\), then find matrix X such that XA = B.
Solution:

Question 10.
Find matrix X, if AX = B, where A = \(\left[\begin{array}{ccc}
1 & 2 & 3 \\
-1 & 1 & 2 \\
1 & 2 & 4
\end{array}\right]\) and B = \(\left[\begin{array}{l}
1 \\
2 \\
3
\end{array}\right]\)
Solution: