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Question

Let M be a matrix such that M×[2103]=[47] Find M

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Solution

M×[2103]=[47]

Order of [2103] is 2×2

Order of [47] is 1×2

Two matrices can be multiplied if:

The number of columns of the 1st matrix must equal the number of rows of the 2nd matrix.

And the result will have the same number of rows as the 1st matrix, and the same number of columns as the 2nd matrix.

M must be 1×2 matrix.

[M]1×2×[2103]2×2=[47]1×2

[xy]1×2×[2103]2×2=[47]1×2 for x,yR

2x+0=4x=2

x+3y=73y=7x=72=9

y=93=3

x=2,y=3

M=[23]

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