Pts will be awarded to those who answer and explain the best. many thanks friend

Question

Pts will be awarded to those who answer and explain the best. many thanks friends

Each statement in Exercises 33-38 is either true (in all cases) or false (for at least one example). If false, construct a specific example to show that the statement is not always true. Such an example is called a counterexample to the statement. If a statement is true, give a justification. (One specific example cannot explain why a statement is always true. You will have to do more work here than in Exercises 21 and 22.) If v1, v2, v3 are in R3 and v3 is not a linear combination of V1, V2, then {v1, V2, v3} is linearly independent.

Explanation / Answer

That is not true. Mainly, because nothing is said about v1 and v2.

So take for example v1=(1,1,1) and v2=(2,2,2). Take v3=(0,0,1). Clearly v3 is not a linear combination of v1 and v2, but the set

{v1,v2,v3} is linearly dependent since 2*v1+(-1)*v2+0*v3=0.

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