Mark the statement 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 the statement is true, give a justification. if v1,…,v4 are in r4 and {v1,v2,v3} is linearly dependent then {v1,v2,v3,v4} is also linearly dependent.
select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
(a) true. because v3 = 2v1 + v2, v4 must be the zero vector. thus, the set of vectors is linearly dependent.
(b) true. the vector v3 is a linear combination of v1 and v2, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.
(c) true. if c1 =2, c2 = 1, c3 = 1, and c4 = 0, then c1v1 + + c4v4 =0. the set of vectors is linearly dependent.
(d) false. if v1 = v2 = v3 = and v4 = [1 2 1 2], then v3 = 2v1 + v2 and {v1, v2, v3, v4} is linearly independent.

Answer with Step-by-step explanation:

We are given that are in and is linearly dependent then {v_1,v_2,v_3,v_4}[/tex] is also linearly dependent.

We have to find that given statement is true or false.

Dependent vectors:Dependent vectors are those vectors in which atleast one vector is  a linear combination of other given vectors.

Or If we have vectors

Then their linear combination

There exist at least one scalar which is not zero.

If are dependent vectors then

for scalars

Then , by definition of dependent  vectors

There exist a vector which is not equal to zero

If vector is a linear combination of , So at least one of vectors in the set is a linear combination of others and the set is linearly dependent.

Hence, by definition of dependent vectors

{} is linearly dependent.

Option B is true.

irrational, then, just means all the numbers that aren't rational. every integer is a rational number, since each integer n can be written in the form n/1. however, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.

step-by-step explanation:

answer: b

step-by-step explanation: im sorry bro bro but thats not a eqation the human mind can answer and plus im a devil