I am still baffled on how I can prove if something is a solution to = (Matrix Equation). Do I need to know how to solve its matrix first despite having a lacking amount of given values?
An example scenario would involve:
If 1 and 2 are solutions to the linear system =, then w = 1/4u1 +3/4u2 is also a solution to Ax =b.
Thus, how can I prove if this statement is true or false?
Your responses would indeed help me a lot on this one as I am freshly exposed with this part about matrix equations. Thank you very much!
If $u_1 $ and $u_2$ are solutions to the linear system $ =$ then $$Au_1=b,\quad Au_2=b$$ $$\Rightarrow Aw=A(\frac{1}{4}u_1+\frac{3}{4}u_2)=\frac{1}{4}Au_1+\frac{3}{4}Au_2=b$$ All you need is $Ac=cA$ for any scalar c