Question

If A = `[(3, -2)]` and B = `[(-1, 4),(2, 0)]`

Assertion (A): Product AB of the two matrices A and B is possible.

Reason (R): Number of columns of matrix A is equal to number of rows in matrix B.

विकल्प

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is incorrect reason for A.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Let's verify the assertion and reason given the matrices A and B:

Given matrices:

A = `[(3, -2)]` 

B = `[(-1, 4),(2, 0)]`

Assertion (A):

The product AB of the two matrices A and B is possible.

Reason (R):

The number of columns of matrix A is equal to the number of rows in matrix B.

Verification:

1. Matrix dimensions:

• Matrix A has dimensions 1 × 2 (1 row, 2 columns).
• Matrix B has dimensions 2 × 2 (2 row, 2 columns).

2. Condition for matrix multiplication:

• For the product AB to be defined, the number of columns in matrix A must be equal to the number of rows in matrix B.

3. Check the condition:

• Matrix A has 2 columns.
• Matrix B has 2 rows.
• Since the number of columns in A is equal to the number of rows in B, the matrix product AB is possible.