Let S be a subset of an n-dimensional vector space V, and suppose S contains fewer than n vectors. Explain why S cannot span V.

Q: The set of vectors in R? with y = -3x is a real vector space

A:

Q: State if the following statement is true or false: If y is a vector space of dimension , then any…

A: Given:

Q: The set ((x,y) : × 20, y 20) with the standard operations in R in not a vector space.

A:

Q: Label the following statements as true or false, and give a brief justification If V is a vector…

A: True. If possible let S be linearly independent with n vectors but do not span V

Q: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set {v1 − 2v2,…

A:

Q: Consider the vector space V with dimension = n, then any set of V with more than n vectors should be…

A: Remark: Let V is a vector space of dimension n, then any linearly independent set of vectors in V…

Q: Let u and v be distinct vectors in a vector space V. Show that {u, v} is linearly dependent if and…

A: We have to show:Let u,v ∈ V , u ≠ v.{u,v}  is linearly dependent <=> u or v is multiple of…

Q: If V is the space of all vectors in R*that are orthogonal to W = Span{(1,0,2,1), (0,0,1,5)}, then…

A:

Q: If a vector space V contains 4 linearly independent vectors, then dim(V) > 4. true false

A: Given ,  If a vector space V contains 4 linearly independent vectors , then  We have to check dim(V)…

Q: Let V be the set of all polynomials over Q of degree 2 together withthe zero polynomial. Is V a…

A:

Q: Let V be a vector space with inner product.  Suppose S is a subset of V and is linearly independent,…

A: We are given that V is a vector space with inner product and S is a subset of V. Also, S is linearly…

Q: Prove that a subset of a linearly independent vector set is linearly independent.

A: First of all,Let the set S= {v1, v2, v3, ……, vn} be a linearly independent set.Now, it is required…

Q: Linear algebra

A:

Q: Show that W is a vector space.

A:

Q: Can a vector in a vector space R -4 - 2 be 2. span by -1 2 イ

A: Span of vectors.

Q: 3/ Given a vector x, show that the infinity norm defined by || X 1100 = max | X₁ Do Ksign

A: Given a vector X A norm is a function such that the following conditions hold ∥x∥≥0 ∀x∈Rn ∥x∥=0 if…

Q: Prove that any nonempty subset of a linearly independent set of vectors {v1, . . . , vn} is also…

A:

Q: Let (V, (, )) be an inner product space and let v, w be vectors in V. If (v, w) = 7 and w = 5, then…

A:

Q: Let S be a finite minimal spanning set of a vector space V . That is, S has the property that if a…

A:

Q: Every linearly dependent subset of a vector space V contains the zero vector. O True False

A: We have to see the given statements is true or false.

Q: Determine the dimension of the vector space. R9

A:

Q: Let {v1, . . . , vn} be a spanning set for the vector space V, and let v be any other vector in V.…

A:

Q: Let V be a vector space and u and w be vectors in V. Prove that {u, w} is linearly independent if…

A: Linearly independent sets: A set of vectors {v1,v2.......vn} is said to be linearly independent if…

Q: Let v1 , v2 , . . . , vn be linearly independent vectors in a vector space V. Show that v2, . . . ,…

A: If the given vectors are linearly independent in the vector space V. Then it follows that

Q: Define vector space and determine whether the set of all positive real numbers u with the operations…

A:

Q: Show that the set is a sub-vector space of space R3 and find the generator set of this sub-vector…

A: A typical vector in H = (2t, t - k, -2t + 3k) = (2t, t, -2t) + (0, -k, 3k) = t(2, 1, -2) + k(0, -1,…

Q: Determine whether the set, together with the standard operations, is a vector space. If it is not,…

A:

Q: snip

A: If v = <a, b> is an algebraic vector whose initial point is the origin, then v is called…

Q: Find the dimension of the vector space.R6

A:

Q: -2 Show whether or not the vector bs is a linear combination of the vectors a, = az = and az = that…

A:

Q: w that the space V = {(x1, x2, x3) ∈F3

A: To prove that the space V=(x1, x2, x3)∈F3|x1+2x2+2x3=0 forms a vector space.

Q: Find the norm of x and the unit vector ü in the direction of x if ||| = u =

A:

Q: Let {v1, v2, . . . , vk} be a linearly independent set of vectors in a vector space V. Delete the…

A:

Q: 2. Show that if the orthogonal dimension of a Hilbert space H is finite, it equals the dimension of…

A: Given: Finite dimension To find: Former finite

Q: State if the following statement is true or false: If y is a vector space of dimension , then any…

A: Statement is False.

Q: The vector space of dimension n should have a basis set with at least n vectors Select one: O True O…

A: The vector space of dimension n should have a basis set with at least n vectors.

Q: Find the dimension of the vector space.P4

A: Here the given vector space V= P4 or

Q: Show that if V is a real vector space and av=0, then a=0 or v=0

A:

Q: The vector spaces M2, 2 and M5,1 are isomorphic to each other ylgn ihi

A: False

Q: Let X be the vector space of all or Can we obtain the norm defined on from an inner product?

A:

Q: Let u and v be vectors in an inner product space V. If ((u − v), (u + v)) = 0, show that u=v.

A: Given, u and v be vectors in an inner product space V. ((u − v), (u + v)) = 0

Q: Which of the following vector spaces has a different dimension? O M23 O R O M32

A: First we have to find the dimension of all vector space.

Q: Let (V, (, )) be an inner product space and let v, W be vectors in V. If (v, w) : = 7 and |w| = 5,…

A:

Q: If V is the space of all vectors in R*that are orthogonal to W = Span{(1,0,2,1),(0,0,1,5)}, then…

A:

Q: 49. Show that in the vector space V, (R), the vectors (1, 2, 3), (- 2, 1, 4), (- 1, – 1/2, 0) form a…

A: We prove that the set of vectors form a linearly dependent set.

Q: Consider the vector space V with dimension = n, then any set of V with exactly n vectors should be…

A: The given statement is FALSE

Q: Let x, y, and z be vectors in a vector space V. Prove that if x + y = x + z then y = z.

A: if, x+y=x+z we use transportation and solve it

Q: The dimension of the vector space of M, is 25. Select one: O True O False

A: Given that: Dimensions of the vector space of M5 is 25.

Q: Let V be a vector space, and let -u and -w be nonzero vectors in V. Prove that if ~u and -w are…

A: Let V be a vector space and let u and v be two nonzero vectors in V. To prove: if u and v are…

Q: Pn, +,) is a vector space

A: In this question, we need to prove (Pn, +,.)  is vector space. For this, we have to show all 9…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.