Question

suppose that B is a matrix whose third column is the sum of the first two columns,then the third column of AB is
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Answer 1

Given that,

B is a matrix and third column of B is sum of the first two columns.

We know that,

The column third of B is sum of previous two columns of B.

It means row vector $x=x(i)$ of B satisfies the linear relation.

$x_{3}=x_{1}+x_{2}$

So, we can say that the matrix's rows AB are all linear combination of the rows of B which is satisfies this lines relation.

So, column third is the same combination of previous two columns of AB.

Hence, This is proved.

Answer 2

Answer:

Step-by-step explanation: