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Suppose P and Q are two different matric...

Suppose P and Q are two different matrices of order 3 ` xx n and n xx p ` ,then the order of the matrix `P xx Q ` is ?

A

` 3 xx p `

B

` p xx 3 `

C

` n xx n`

D

` 3 xx 3 `

Text Solution

AI Generated Solution

The correct Answer is:
To find the order of the matrix product \( P \times Q \), we need to follow these steps: ### Step 1: Identify the orders of matrices P and Q - Matrix \( P \) is of order \( 3 \times n \). - Matrix \( Q \) is of order \( n \times p \). ### Step 2: Check the condition for matrix multiplication For two matrices to be multiplied, the number of columns in the first matrix must equal the number of rows in the second matrix. - Here, \( P \) has \( n \) columns and \( Q \) has \( n \) rows. - Since both are equal, the multiplication \( P \times Q \) is valid. ### Step 3: Determine the order of the resulting matrix The order of the resulting matrix from the multiplication of two matrices is determined by the number of rows in the first matrix and the number of columns in the second matrix. - The resulting matrix \( P \times Q \) will have: - Rows from \( P \): 3 - Columns from \( Q \): \( p \) Thus, the order of the matrix \( P \times Q \) is \( 3 \times p \). ### Final Answer The order of the matrix \( P \times Q \) is \( 3 \times p \). ---
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