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]\), R_{1} ↔ R_{2}

(ii) \(\left[\begin{array}{cc}

2 & 4 \\

1 & -5

\end{array}\right]\), C_{1} ↔ C_{2}

(iii) \(\left[\begin{array}{ccc}

3 & 1 & -1 \\

1 & 3 & 1 \\

-1 & 1 & 3

\end{array}\right]\) 3R_{2} and C_{2} → C_{2} – 4C_{1}

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: