Determine if the column vectors [2,1,3,4]' [1,1,1,1]' and [5,3,7,9]' are linearly independent

Expert Solution

Colby Messinger answered 2 years ago

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 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

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)

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)}

Let ?1=(1,0,1,0) ?2=(0,−1,1,−1) ?3=(1,1,1,1) be linearly independent vectors in ℝ4. a. Apply the Gram-Schmidt algorithm to...

Let ?1=(1,0,1,0) ?2=(0,−1,1,−1) ?3=(1,1,1,1) be linearly independent vectors in ℝ4. a. Apply the Gram-Schmidt algorithm to orthonormalise the vectors {?1,?2,?3} of vectors {?1,?2,?3}. b. Find a vector ?4 such that {?1,?2,?3,?4} is an orthonormal basis for ℝ4 (where ℝ4 is the Euclidean space, that is, the inner product is the dot product).

There are three vectors in R4 that are linearly independent but not orthogonal: u = (3,...

There are three vectors in R4 that are linearly independent but not orthogonal: u = (3, -1, 2, 4), v = (-2, 7, 3, 1), and w = (-3, 2, 4, 11). Let W = span {u, v, w}. In addition, vector b = (2, 1, 5, 4) is not in the span of the vectors. Compute the orthogonal projection bˆ of b onto the subspace W in two ways: (1) using the basis {u, v, w} for W, and...

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.

Find all the vectors in R4 that are perpendicular to the three vectors <1,1,1,1>, <1,2,3,4>, and...

Find all the vectors in R4 that are perpendicular to the three vectors <1,1,1,1>, <1,2,3,4>, and <1,9,9,7>

T or F 1) Any N vectors spanning R^n are linearly independent 2)R5 has 7 linearly...

T or F 1) Any N vectors spanning R^n are linearly independent 2)R5 has 7 linearly independent vectors 3) If a set of vectors with n elements is linearly dependent, then a set with n - 1 elements is also linearly dependent 4) There exists a Linear Function T:R^n -> R^n such that the range and the kernel of T are equal. 5) If a vector space has a dimension of n, then a basis for the vector space will...

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