Question 1

Question 1: Apply the given elementary transformation on each of the following matrices. A = , R1 ↔ R2

Accepted Answer

A = By R1 ↔ R2, we get, A ~

Question 2

Question 2: B = , R1 → R1 → R2

Accepted Answer

B = , R1 → R1 → R2 gives, B ~

Question 3

Question 3: A = , C1 ↔ C2; B = , R1 ↔ R2. What do you observe?

Accepted Answer

A = By C1 ↔ C2, we get, A ~ …(1) B = By R1 ↔ R2, we get, B ~ …(2) From (1) and (2), we observe that the new matrices are equal.

Question 4

Question 4: A = , 2C2 B = , -3R1 Find the addition of the two new matrices.

Accepted Answer

A = By 2C2, we get, A ~ B = By -3R1, we get, B ~ Now, addition of the two new matrices

Question 5

Question 5: A = , 3R3 and then C3 + 2C2.

Accepted Answer

A = By 3R3, we get A ~ By C3 + 2C2, we get, A ~ ∴ A ~

Question 6

Question 6: A = , C3 + 2C2 and then 3R3. What do you conclude from Ex. 5 and Ex. 6 ?

Accepted Answer

A = By C3 + 2C2, we get, A ~ ∴ A ~ By 3R3, we get A ~ We conclude from Ex. 5 and Ex. 6 that the matrix remains same by interchanging the order of the elementary transformations. Hence, the transformations are commutative.

Question 7

Question 7: Use suitable transformation on into an upper triangular matrix.

Accepted Answer

Let A = By R2 – 3R1, we get, A ~ This is an upper triangular matrix.

Question 8

Question 8: Convert into an identity matrix by suitable row transformations.

Accepted Answer

Let A = By R2 – 2R1, we get, A ~ By R2, we get, A ~ By R1 + R2, we get, A ~ This is an identity matrix.

Question 9

Question 9: Transform into an upper triangular matrix by suitable row transformations.

Accepted Answer

Let A = By R2 – 2R1 and R3 – 3R1, we get A ~ By R3 – R2, we get, A ~ This is an upper triangular matrix.

Chapter 2 Matrices Ex 2.1 Solutions