Let S ={v1 , v2 , v3 } be a set of nonzero vectors in R3 such that any two vectors in S are orthogonal. Prove that S is linearly independent.

Q: Let u and v be non-zero vectors in 3-space. Prove that u and v are perpendicular if and only if |u…

A:

Q: Let A and B be vectors in R. Show that ||A|| = || B|| if and only if A+ B is orthogonal to Ã- B.

A: To solve the given orthogonality problem related to vector.

Q: Show that the vectors (3+ /2,1+V2) and (7, 1 +2\/2) in R² are linear!ly dependent over R but…

A:

Q: 2. Show that if the vectors v,, v2, .,Vm are mutually orthogonal then they are linearly ...…

A:

Q: Find all values of a such that the vectors = and are perpendicular

A: Given:The vectors are  and  are perpendicular.To Find:The value of .Concept Used:When two vectors…

Q: Let u, v, w be three linearly independent vectors in R7. Determine a value of k, k = so that the set…

A: Linearly independent is defined as the rank of the given matrix being equal to the number of…

Q: Which of the following vectors are linearly independent? Non of these

A: We want to find independent vectors.

Q: 3 2 (c) 1 2 -2 -2 N NO

A: Question is solved.

Q: Find the vector z, given that u- (9, 2, 7), 2,-1), andw = 0,-4

A:

Q: Prove that, if two of the vectors V₁, V2,..., Vp are equal, then the vectors are early dependent.

A:

Q: Is the following set of vectors linearly independent? {·O·} 2 0 5 6

A:

Q: Let A, B, C, D be points in 3-space with position vectors a, b, c, d respectively such that b – a =…

A:

Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

A:

Q: Find the value of u that make the set of vectors {a, b, c, d} linearly dependent. [1 2 1 1] b = [0 1…

A:

Q: Suppose V1, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(v1, V2, V3) such…

A: Here, v1,v2,v3 is an orthogonal set of vectors in R5 and w is a vector in Span(v1,v2,v3) such…

Q: 2 Consider A = -2 null(A). 4 2 2 4 -4 -2 -2 -4 -2 0 1 Give a set of vectors that spans each of im(A)…

A:

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: First we will express vector s1 a linear combination of other vectors s2 and s3soing so will give us…

Q: Le and ü .Write j as the sum of two orthogonal vectors, a, in Span {u} and i2 orthogonal to ū.

A:

Q: Let v and w be nonzero vectors in R³ such that the equation XXV = W is satisfied by at least seven…

A: Given v and w are nonzero vectors in ℝ3 such that x×v=w is satisfied by at least seven distinct…

Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3) such…

A:

Q: Suppose V₁, V₂, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V₁, V2, V3 )…

A:

Q: 2 -7' Let j = and u .Write j as the sum of two orthogonal vectors, , in Span {u} and 2 orthogonal to…

A: