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Q.

If A is of order m×n, B is of order 3×p and C is of order 2×4. If AB+C is defined then the value for m = ____, n=[[2]] and p=[[3]].

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Detailed Solution

Matrix multiplication is possible if and only if column no. of the first matrix is same as row no. of second matrix.
A is of order m x n, B is of order 3xp we want A.B must be defined
So, column no. of matrix A is the same as row no. of matrix B.
Here, column no. of matrix A = n =row no. of matrix B=3

∴ n = 3

Order of matrix AB is mx p
We want AB +C is defined
Addition of two matrices is possible only if two matrices are of the same order.
C is the matrix of order 2 x 4
AB is of order m x p= 2 x 4

∴ m = 2, p = 4

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