Question

Consider the following vectors v1 = [1; 0; 1; 0], v2 = [0; 1; 0; 1], v3 = [0; 1; 2; 3], v4 = [1; 2; 3; 4] Determine if the following hold: The dimension of span{v1, v2, v3} is 3 v1, v2, v3, v4 form a basis of R^4 2. (3 pts) Determine if the following statement if true or false. An answer without supportive argument will yield at most 1/3 of the credit. "Let a, b, c be 3 vectors from a vector space V. Define two subspaces U=span{a,b,c}, W=span{a-2b,b,a+c}. Then it must be that U=W" Hint: You should ask yourself two questions: Is U contained in W? Is W contained in U?

          Consider the following vectors
v1 = [1; 0; 1; 0], v2 = [0; 1; 0; 1], v3 = [0; 1; 2; 3], v4 = [1; 2; 3; 4]

Determine if the following hold:
The dimension of span{v1, v2, v3} is 3
v1, v2, v3, v4 form a basis of R^4

2. (3 pts)
Determine if the following statement if true or false. An answer without supportive argument will yield at most 1/3 of the credit.
"Let a, b, c be 3 vectors from a vector space V. Define two subspaces U=span{a,b,c}, W=span{a-2b,b,a+c}. Then it must be that U=W"
Hint: You should ask yourself two questions: Is U contained in W? Is W contained in U?

Consider the following vectors
v1 = [1; 0; 1; 0], v2 = [0; 1; 0; 1], v3 = [0; 1; 2; 3], v4 = [1; 2; 3; 4]

Determine if the following hold:
The dimension of spanv1, v2, v3 is 3
v1, v2, v3, v4 form a basis of R^4

2. (3 pts)
Determine if the following statement if true or false. An answer without supportive argument will yield at most 1/3 of the credit.
"Let a, b, c be 3 vectors from a vector space V. Define two subspaces U=spana,b,c, W=spana-2b,b,a+c. Then it must be that U=W"
Hint: You should ask yourself two questions: Is U contained in W? Is W contained in U?

Added by Pablo E.

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