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For each subspace in Exercises 1–8, (a) find a basis, and (b) state the dimension.$$\{(a, b, c) : a-3 b+c=0, b-2 c=0,2 b-c=0\}$$
a. the subspace S has no basis.b. 0
Calculus 3
Chapter 4
Vector Spaces
Section 5
The Dimension of a Vector Space
Vectors
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we'll get something. This problem were given subspace. That is a B C D. Where? A minus three B. Let's see. Zero. So by this equation, we know that see can be represented as freebie minus a So that means C can be determined by being a so our vector a B c D can be re read. Could be right. We can rewrite this vector. Um, terms off, eh? Hey, freebie mind, say, and the so. I noticed that A, B and D R V variables here. Well, c can be represented as, uh, A and B. So keep going. We can separate the specter so that it will be 10 91. I'm a skater. Eight and zero. 13 zero. Time Specter beak. And for the vector d off. Sorry. Should be scaler instead of Victor. Um, times of skated be And poor skater d we have There was 00 times skater d All right, so our pieces will be these three vectors. 10 negative. 10 013 and 0001 All right, So this is our faces and our dimension of this subspace. Well, the three
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