Question

If A is a matrix of order 1×3 and B is a matrix of order 3×4, then order of the
matrix obtained on multiplying A and B is
(a) 3×3 (b) 4×1 (c) 3×4 (d) 1×4

Answer 1

Answer:

The order of matrix obtained in multiplying the matrices 'A' and 'B' is (1 × 4).

Step-by-step explanation:

Given,

The order of matrix 'A' is 1 × 3

The order of the matrix 'B' is 3 × 4

To find,

The order of obtained by multiplying the matrices 'A' and 'B' (AB).

Concept,

If two matrices of order (a × b) and (c × d) are multiplied then the order of the matrix obtained is (a × d), provided b = c.

Calculation,

For matrix 'A'

The order is (1 × 3)

Here a = 1, and b = 3

For matrix 'B'

The order is (3 × 4)

Here c = 3, and d = 4

As clearly we can see that b = c = 3

Then the order of matrix obtained in multiplying the matrices 'A' and 'B' is (a × d) = (1 × 4).

Answer 2

Answer:

Option (d) is correct.

Step-by-step explanation:

Concept:-

• The multiplication of the matrices is possible if and only if the number of columns of the matrix A is equal to the number of rows of the matrix B.

• If the order of the matrix A is n × m and the order of the matrix B is m × r, then the order of the matrix AB is n × r.

Given:-

The order of the matrix A is 1 × 3.

The order of the matrix B is 3 × 4.

To find:-

The order of the matrix obtained on multiplying A and B, i.e.,

The order of the matrix AB.

Since the number of columns in the matrix A is 3.

And the number of the rows in the matrix B is 3.

Thus, the multiplication of the A and B exists.

Then,

The order of the matrix AB is,

= Number of rows of the matrix A × Number of columns of the matrix B

= 1 × 4

Therefore, option (d) is the correct answer.

Rest all other options are incorrect.

Final answer: Option (d) is correct.

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