Let X,Y be a finite dimension vector space then O dim(x)=dim(Y) O dim(X)

Q: The linear map A:R^4->R2[t] is defined by A(x,y,z,u)->(x-z)t. Then the dimension of the kernel…

A: We need to find the dimension of the kernel of the given map, A:R4→R2​[t] defined by…

Q: Find a condition on a, b, c so that (a, b, c)  ∈ R^3, belongs to the space spanned by →u = (2, 1,…

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Q: 3) Vector spaces can be defined where the sets of scalars are different from R and C. For example,…

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Q: 1. True/false: all linear functions U:M_(3x2)(F)->F^6 are isomorphisms. 2. True/False: If P and Q…

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Q: 6. Determine if {(x, y): x^2 + y^2 ≥ 8} is a subspace of R^2

A: The given set is {(x, y) | x2 + y2 ≥ 8}. We check whether the set is a subspace of R2.  Since the…

Q: Which of the following sets is not a subspace of the space R^3? (a) R^3. (b) Any plane passing…

A: Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: Determine whether the given set S is a subspace of the vector space V. DA. V = C5 (I), and S is the…

A: A subset S of vector space V is said to be a subspace of V if it is closed under vector addition and…

Q: Consider the vector space R^n with inner product

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Q: ctor space? If not, why not? 7. Let C denote the set of all convergent sequences of real numbers…

A: see attachments pls

Q: The set {(x, , x,)' 1 x,+ x, =0} form a subspace of R Select one: O True False

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Q: Which of the listed subsets of the vector space R^3 is homogeneous but not additive?

A: option bExplanation:

Q: 10. Show that V = R² with the standard scalar multiplication, but addition defined by (x, , y.) +…

A: We have to show that the set V with the addition operation x1, y1+x2, y2=x13+x233, y13+y233 and…

Q: (a) What is the nullspace of the identity matrix? (b) Give a 3 × 3 matrix whose nullspace is the x…

A: (a) Let    be  an    matrix.   Then, the null space of the matrix  A  is  denoted  by  null(A)  and…

Q: Let F = Z3 be the field with three elements. Which of the following vectors from the vector space…

A: The correct option is:c) (2,0,2)Explanation:

Q: Show that for any vector u in R^n, (u^(T))*(u) = 0 if and only if u = 0.

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Q: Show that ℓ^1 is a normed linear space.

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Q: HIf vectors x, y, z, u in the real vector space p (the polynomials) are defined by x(t)=1, y (t)=t,…

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Q: : R^3-->R^3,T(x, y, z) = ( x + y, y + z, x - z)  (a)the basis of  the range(T) (b)determine if T…

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Q: 2. Let M be the collection of all 2 × 2 real matrices. If define a b ^ - (**) EM A= C d |A| = and…

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Q: Compute the flux of the vector field (x², - xy³), out of the rectangle with vertices (0,0), (5,0),…

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Q: Let C[0, 1] be the vector space of continuous functions that are defined on the interval [0, 1].…

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Q: TRUE or FALSE  If v + w is a vector space, then v and w are also in the vector space  The union of…

A: Note:- As per our guidelines, we can answer the first three sub-parts of this problem. Please…

Q: Which of the following mappings does not define a linear transformation A: R^3 -> R^2?

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Q: a) Is the set W = {(x, y, 1) | x, y are real numbers} a subspace of R^3 ? (b) Is the set W = {(x,…

A: Subspace test:  Let V be a vector space and W is a subset. The subset W is said to be subspace if it…

Q: Determine whether the set equipped with the given operations is a vector space. For those that are…

A: Given set of ordered pairs of the form (7,x). To verify t is a vector space under the given…