Hey guys i need help with both of these questions NO LINKS AND NO DOING IT JUST FOR POINTS if you answer both correctly showing
work i will give brainliest thanks and remember i need both answers shown with work
2 answers:
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Answer:
Step-by-step explanation:
given that U, V are two vectors in R^n
These two vectors can be written as a linear combination of 3 vectors
w1, w2, and w3
To prove that U+V also can be written as a linear combination of these three vectors.
Since U is a linear combination we can write for not all a,b, c equal to 0
Similarly for d,e,f not all equal to 0
Adding these we have
Here all a+d, b+e or c+f cannot be simultaneously 0.
So we get U+V can be written as a linear combination of w1, w2 w3 as follows:
Proved