t779
13.02.2020 •
Mathematics
Let Bold u comma Bold v comma Bold w 1 comma Bold w 2 comma and Bold w 3 be vectors in Bold Upper R Superscript n. If u and v can both be written as linear combinations of Bold w 1 comma Bold w 2 comma and Bold w 3, show that u+v can also be written as a linear combination of Bold w 1 comma Bold w 2 comma and Bold w 3.
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Ответ:
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
Ответ:
136/17 = 8
8 * 9 = 72 / 2 = 36
8*8 = 64 / 2 = 32
32 +32 + 36 + 36 = 136
the rectangle is 36 x 32