Question

Linear algebra: row reduce

make second row all zeros

1 2

4 3

Answer 1

make second row all zeros

1 2

4 3

As per the given criteria, it is equivalant that both rows are linearly dependent. i.e we should be able to express second row in multiples of first row in order to do that.

So, it can be written as,

(1x+2y) = K(4x+3y)

There should exist a K value.

So, we have 3 variables and 1 equation, which is only possible at x = 0 and y = 0. Which is 0 vector or 0 equation.

So, there is no possibility that we can reduce row2 to all zeros as both equations are not parallel or both vectors are not linear.

We can reduce R2 to R2-4R1 (or) R2-1.5R1 to make any 1 element as 0 but two elements 0 is not possible at one operation.