# 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: