Please do not copypaste from another question Please show yo

*Please do not copy/paste from another question. Please show your own method.

Solution

Now note that only column of A that has a non zero third row entry is 2nd column

So if b were to lie in span of columns of A

Then third row element of b will be generated by second column alone

Denote first second and third columns by: C1,C2,C3 respectively

Let, a,b,c so that

aC1+bC2+cC3=b

So, b=3 comparing third row coefficients

2a+3+c=2 ie 2a+c=-1

4a+3*3+c=6   ie 4a+c=-3

HEnce, 2a=-2 ie a=-1

2a+c=-1

c=-1-2a=-1+2=1

So, b is in the span(A)