Question

In: Advanced Math

Determine whether each set of vectors is linearly dependent or linearly independent. a) (1,1,0,1), (1,0,1,1), (0,1,1,1)...

Determine whether each set of vectors is linearly dependent or linearly independent.

a) (1,1,0,1), (1,0,1,1), (0,1,1,1)

b) (1,0,1,0), (0,1,0,1), (1,-1,1,-1), (1,-1,0,0)

Solutions

Expert Solution


Related Solutions

1. Determine each of the following set of vectors is linearly independent or dependent. (a) S1...
1. Determine each of the following set of vectors is linearly independent or dependent. (a) S1 = {(1, 2, 3),(4, 5, 6),(6, 9, 12)}. (b) S2 = {(1, 2, 3, 4),(5, 6, 7, 8),(3, 2, 1, 0)}. (c) S3 = {(1, 2, 3, 4),(5, 6, 7, 8),(9, 10, 11, 12)}
Determine whether the members of the given set of vectors are linearly independent. If they are...
Determine whether the members of the given set of vectors are linearly independent. If they are linearly dependent, find a linear relation among them of the form c1x(1) + c2x(2) + c3x(3) = 0. (Give c1, c2, and c3 as real numbers. If the vectors are linearly independent, enter INDEPENDENT.) x(1) = 9 1 0 , x(2) = 0 1 0 , x(3) = −1 9 0
For each family of vectors, determine wether the vectors are linearly independent or not, and in...
For each family of vectors, determine wether the vectors are linearly independent or not, and in case they are linearly dependent, find a linear relation between them. a) x1 = (2, 2, 0), x2 = (0, 2, 2), x3 = (1, 0, 1) b) x1 = (2, 1, 0), x2 = (0, 1, 0), x3 = (1, 2, 0) c) x1 = (1, 1, 0, 0), x2 = (0, 1, 1, 0), x3 = (0, 0, 1, 1), x4 =...
Determine all values of a for which the following set of vectors is dependent or independent....
Determine all values of a for which the following set of vectors is dependent or independent. You can select 'always', 'never', 'a = ', or 'a ≠', then specify a value or comma-separated list of values. ⎧ ⎪ ⎨ ⎪ ⎩⎫ ⎪ ⎬ ⎪ ⎭a001, 12−2−2, 48−8−9Dependent: When a = 0Independent: When a ≠ 0
Determine if the column vectors [2,1,3,4]' [1,1,1,1]' and [5,3,7,9]' are linearly independent
Determine if the column vectors [2,1,3,4]' [1,1,1,1]' and [5,3,7,9]' are linearly independent
A basis of a vector space V is a maximal linearly independent set of vectors in...
A basis of a vector space V is a maximal linearly independent set of vectors in V . Similarly, one can view it as a minimal spanning set of vectors in V . Prove that any set S ⊆ V spanning a finite-dimensional vector space V contains a basis of V .
Prove the follwing statements Suppose that S is a linearly independent set of vectors in the...
Prove the follwing statements Suppose that S is a linearly independent set of vectors in the vector space V and let w be a vector of V that is not in S. Then the set obtained from S by adding w to S is linearly independent in V. If U is a subspace of a vector space V and dim(U)=dim(V), then U=V.
if {v1,v2,v3} is a linearly independent set of vectors, then {v1,v2,v3,v4} is too.
if {v1,v2,v3} is a linearly independent set of vectors, then {v1,v2,v3,v4} is too.
In each of the following situations, identify the independent variable and dependent variable. Determine whether the...
In each of the following situations, identify the independent variable and dependent variable. Determine whether the growth is linear or exponential and explain why by the definition of linear and exponential growth (Do not present the table) a) The price of gasoline has been rising 2% per month. b) The total cost of a taxi ride increases by $ 5 per 2 miles. c) The population of a bacteria is double every 20 hours.
Determine whether the following pairs of functions are linearly independent or not on the whole real...
Determine whether the following pairs of functions are linearly independent or not on the whole real line. Determine whether the following pairs of functions are linearly independent or not on the whole real line. BEWARE: You only get 3 tries. Linearly dependent * 1. f(theta) = 14 cos 3theta and g(theta) = 56cos^3 theta - 42 cos theta. Linearly dependent  2. f(t) = t^2 + 14t and g(t) = t ^2 - 14t Linearly dependent  3.f(t)=t and g(t)=|t|
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT