What do you observe? A = 1 2 - 1 0 1 3 , 2 C 2 B = 1 0 2 2 4 5 , - 3 R 1 Find the addition of the two new matrices.

The given matrix is A = 1 2 - 1 0 1 3 . Apply the given transformation C 2 → 2 C 2 by multiplying the elements of matrix A in the second column with 2 . If the elements of i th row or column are multiplied by a non-zero number k , then it is denoted as R i → kR j or C i → kC j . Let P be the new matrix after transformation so, P = 1 2 × 2 - 1 0 1 × 2 3 P = 1 4 - 1 0 2 3 Apply the given transformation R 1 → - 3 R 1 by multiplying the elements of matrix B in the first row with - 3 . Let Q be the new matrix after transformation so, Q = 1 × - 3 0 × - 3 2 × - 3 2 4 5 Q = - 3 0 - 6 2 4 5 . Add the new matrices P and Q to get the sum of matrix. P + Q = 1 4 - 1 0 2 3 + - 3 0 - 6 2 4 5 = - 2 4 - 7 2 6 8 .

A = 1 - 1 3 2 1 0 3 3 1 , 3 R 3 and then C 3 + 2 C 2 .

The given matrix is A = 1 - 1 3 2 1 0 3 3 1 . A = 1 - 1 3 2 1 0 3 3 1 If the elements of i th row or column are multiplied by a non-zero number k , then it is denoted as R i → kR j or C i → kC j . Now apply the transformation R 3 → 3 R 3 by multiplying the third row of the matrix A with 3 . Let P be the new matrix after transformation so, P = 1 - 1 3 2 1 0 3 × 3 3 × 3 1 × 3 ⇒ P = 1 - 1 3 2 1 0 9 9 3 Apply the given transformation C 3 + 2 C 2 , first multiplying the second column with 2 and then adding the third column of matrix P . Let Q be the new matrix after transformation so, ⇒ Q = 1 - 1 3 + - 2 2 1 0 + 2 9 9 3 + 18 ⇒ Q = 1 - 1 1 2 1 2 9 9 21 . Therefore, the required matrix is 1 - 1 1 2 1 2 9 9 21 .

Use suitable transformation on 1 2 3 4 to convert it into an upper triangular matrix.

Given 1 2 3 4 Apply row transformation to reduce given matrix into an upper triangular matrix. Apply R 2 → R 2 - 3 R 1 = 1 2 3 - 3 × 1 4 - 3 × 2 = 1 2 3 - 3 4 - 6 = 1 2 0 - 2 ⇒ 1 2 0 - 2 is an upper triangular matrix Therefore, the required matrix is 1 2 0 - 2 .

Convert 1 - 1 2 3 into an identity matrix by suitable row transformations.

Given A = 1 - 1 2 3 Apply row transformation on matrix A to reduce it into an identity matrix. Apply R 2 → R 2 - 2 R 1 A = 1 - 1 0 5 Apply R 2 → R 2 5 A = 1 - 1 0 1 Now Apply R 1 → R 1 + R 2 A = 1 0 0 1 = I 2 × 2 Hence matrix A is reduced to an identity matrix through row transformation.

E M B I B E

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Exercise 2.1

Maharashtra Board Solutions for Chapter: Matrices, Exercise 1: Exercise 2.1

Author:Maharashtra Board

Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Chapter: Matrices, Exercise 1: Exercise 2.1

Attempt the practice questions on Chapter 2: Matrices, Exercise 1: Exercise 2.1 with hints and solutions to strengthen your understanding. Mathematics & Statistics (Arts & Science) Part 1 Standard 12 solutions are prepared by Experienced Embibe Experts.

Questions from Maharashtra Board Solutions for Chapter: Matrices, Exercise 1: Exercise 2.1 with Hints & Solutions

EASY

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Exercise 2.1>Q 2

Apply the given elementary transformation on each of the following matrices.

$B = [\begin{matrix} 1 & - 1 & 3 \\ 2 & 5 & 4 \end{matrix}], R_{1} \to R_{1} - R_{2}$

EASY

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Exercise 2.1>Q 3

Apply the given elementary transformation on the following matrix $A = [\begin{matrix} 5 & 4 \\ 1 & 3 \end{matrix}], C_{1} \leftrightarrow C_{2}; B = [\begin{matrix} 3 & 1 \\ 4 & 5 \end{matrix}], R_{1} \leftrightarrow R_{2} .$

EASY

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Exercise 2.1>Q 4

What do you observe?

$A = [\begin{matrix} 1 & 2 & - 1 \\ 0 & 1 & 3 \end{matrix}], 2 C_{2} B = [\begin{array}{l} 1 & 0 & 2 \\ 2 & 4 & 5 \end{array}], - 3 R_{1}$

Find the addition of the two new matrices.

EASY

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Exercise 2.1>Q 5

$A = [\begin{matrix} 1 & - 1 & 3 \\ 2 & 1 & 0 \\ 3 & 3 & 1 \end{matrix}], 3 R_{3}$ and then $C_{3} + 2 C_{2}$ .

EASY

12th Maharashtra Board

IMPORTANT

Mathematics & Statistics (Arts & Science) Part 1 Standard 12>Chapter 2 - Matrices>Exercise 2.1>Q 6

$A = [\begin{matrix} 1 & - 1 & 3 \\ 2 & 1 & 0 \\ 3 & 3 & 1 \end{matrix}], C_{3} + 2 C_{2}$ and then $3 R_{3}$ . What will you conclude if we first do $3 R_{3}$ and then $C_{3} + 2 C_{2}$ .