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If A = [3−2] and B=[−1420]\begin{bmatrix}[r] 3 & -2 \end{bmatrix} \text{ and B} = \begin{bmatrix}[r] -1 & 4 \ 2 & 0 \end{bmatrix}

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.

  1. Assertion (A) is true, but Reason (R) is false.

  2. Assertion (A) is false, but Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Matrices

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Answer

Given, A = [3−2] and B=[−1420]\begin{bmatrix}[r] 3 & -2 \end{bmatrix} \text{ and B} = \begin{bmatrix}[r] -1 & 4 \ 2 & 0 \end{bmatrix}

To multiply two matrices, the number of columns of the first matrix must equal the number of rows of the second matrix.

Matrix A has 1 row and 2 columns.

Matrix B has 2 rows and 2 columns.

So, reason (R) is true.

The number of columns in A is 2 and number of rows in B is also 2.

So, product AB is defined.

So, both A and R are true and R is the correct explanation of assertion A.

Thus, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

Hence, option 3 is the correct option.

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