Question

The rank of 3×3 matrix C(=AB) found by multiplying a non zero column matrix A of size 3×1 and a non zero matrix B of size 1×3 is?

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Answer 1

Answer:

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Explanation:

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Answer 2

Given,

Column A with size $3X1$

Matrix B with size $1 X 3$

To find,

The rank of the matrix got by multiplying A and B

Let the matrix be denoted by C so the rank of C

Solution

The rank of the C is $1$

The rank of the column matrix was $1$.

And, the rank of the row matrix was $1$.

So, the rank of their product cannot be greater than $1$.

As, pre or post- multiplication by a matrix cannot increase rank

Also, the two matrices being non-zero, their product matrix C won't have all elements $0$

So, clearly, the only possible rank of C is $1$.

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