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Mathematics

If [2432]×P=[68]\begin{bmatrix} 2 & 4 \ 3 & 2 \end{bmatrix} \times P = \begin{bmatrix} 6 \ 8 \end{bmatrix}, then the order of matrix P is:

  1. 2 × 2

  2. 2 × 1

  3. 1 × 2

  4. cannot be determined

Matrices

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Answer

Let A = [2432]\begin{bmatrix} 2 & 4 \ 3 & 2 \end{bmatrix}

Let B = [68]\begin{bmatrix} 6 \ 8 \end{bmatrix}

Let order of P be m × n:

Thus, AP = B

For matrix multiplication:

The number of columns in A must equal the number of rows in P.

⇒ m = 2

The order of the product B = Rows of A × Columns of P.

⇒ 2 × 1 = 2 × n

⇒ n = 1.

Order of matrix P = 2 × 1.

Hence, option 2 is the correct option.

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