Let T: R^3 --> R^3 be the linear transformation represented by the matrix in the image. (a) Let ker(T)={v E R^3 | T(v) =0}, the kernel of the linear transformation. Give a description of ker(T). (b) Show that ker(T) is a vector subspace of R^3.

Let T: R^3 --> R^3 be the linear transformation represented by the matrix in the image. (a) Let ker(T)={v E R^3 | T(v) =0}, the kernel of the linear transformation. Give a description of ker(T). (b) Show that ker(T) is a vector subspace of R^3.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Let E= te, e, e be the standard basis for R', let B= (b, bz. b, be a basis for a vector space V. and…

A: Given: Tx1,x2,x3=2x3-x2b1-2x3b2+x1+3x2b3 a. Te1=T1,0,0=0b1+0b2+1b3 Te2=T0,1,0=-1b1+0b2+3b3…

Q: The matrix for an onto linear transformation from \R^4 to \R^3. Find an example

A: Note that: The matrix of the linear transformation from Rn to Rm is of size m × n.

Q: Which one of the following is a subspace of the vector space M2 (R) of 2 x 2 matrices? ss (X) the…

A: .

Q: Find the Kernel and Range of the linear transformation L : R^3 → R^3 defined by L(x) = (x3, 0,…

A: In linear algebra, the kernel of a linear transformation is also known as the "null space." Given a…

Q: Let V = C^3 with the standard inner product. Let T be the linear operator on V whose matrix in the…

A: Given as V=ℂ3 with the standard inner product z1,z2=z1z2

Q: What is the matrix P = (P₁) for the projection of R³ onto the subspace V spanned by the vectors a₁ =…

Q: Which of the following mappings A: R^2->R is a linear functional? (a) (a,b) -> lal + lbl. (b)…

A: Step 1:A linear functional is a linear map from a vector space to its underlying field. Formally,…

Q: Give an example of a non-zero subspace of R^4 which has dimension > 1 and does not contain any of…

A: Consider the example f(x) = {2 + x + x2}, this given polynomial has dimension 3 with the basis {1,…

Q: Let V be the vector space V = Span(e^(2x) , e^(3x) ). Given are the ordend basis defined by: B =…

A: This is a problem of Vector Analysis. One can take it as a problem of Line

Q: What is the relationship between the kernel of a linear transformation from a finite dimensional…

Q: For each matrix A below, describe the invariant subspaces for the induced linear operator T on F^2…

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: Write the equation of a subspace that passes through a point a ∈ R^d and is orthogonal to a given…

A: Let d=3 Now we will find the equation of subspace that passes through a point a€R^3 and orthogonal…

Q: Linear Algebra: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2. Is {p1,p2,p3} a…

A: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2.

Q: a) Let t: R">R be the Composite 3. linear transformation which means the vectors in R? are first…

A: Answer:

Q: Find an orthogonal projection of (6, 0, 0) (1) along the vector (1, 2, 1) (2) On the plane…

A: (1) Let a→=6,0,0, b→=1,2,1 Then orthogonal projection of a→ along the vector b→ is a→·b→b→·b→b→…

Q: IfT: R² R³ is a linear transformation such that -n the standard matrix of Tis 13 T([2])-[3] . and T…

Q: tind the equation of a polynomial Shose graph, passes through the points t-1,7), (0,2)(2;4)

A: As per guidelines I had solved the first question. Thank you.

Q: Let {v1 = (1,2,3,5,9), v2 = (3,1,2,8,9), v3 = (2, -5,5,9,4)} and {u1 = (0,1,1,1,2), u2 = (0,2, -2,…

A: The given question is related with vector space. Given that , v1 = 1,2,3,5,9 , v2 = 3,1,2,8,9 , v3 =…

Q: Let V be a finit dimensions vector space of at least dim =1, Let T: V-> V be a linear transformation…

A: Solution

Q: Let ℝ [x]≤ 2 ---> ℝ be a linear transformation such that T(x2)= -3, T(x2+x)=-4, T(x+1)=-1 What is…

Q: d. Find the transition matrix from C to B. e. Find the coordinates of u = (2, –2) in the ordered…

Q: Let f : R^2 → R^3 be the linear transformation such that f(1, 1) = (0, 1, 2) and f(−1, 1) = (2, 1,…

Q: Let V be a finit dimensions vector space of at least dim =1, Let T: V-> V be a linear transformation…

A: Given that V be a finite dimensional vector space with dimension ≥1 and T: V→V be a linear…

Q: Let M = x2 :¤1, x2 E R X1

Q: A В E 17 Matrix A from Problem 2 (3x5): 18 19 18 1 179 20 7 14 17 141 21 -28 -116 -232 -91 -2316 22…

A: All the subparts of the given question are solved below.

Q: Let A = M. (f) be the matrix associated with the linear map ƒ((x,y,z)) = (x-2y,y+2,0) relative to…

Q: te the above linear system (of one equation) as a homogeneous matrix problem.

Q: W = (x:x= X1 X2 LX3 where x3 = 5x₁ + 8x2

Q: Determine whether the given subset is subspace of R^3 W={(x1,x2,x3):x1+x2+x3=0}

A: Let the subset W is given as W={(x1,x2,x3)| x1+x2+x3=0} Determine whether the given subset is…

Q: Verify all vector space axioms under the given operations (x,y,z)+(x',y'z') = (x+x'+1,y+y'+2,z+z'+3)…

A: The objective of the question is to verify if the given operations satisfy all the axioms of a…

Q: let b={(0,2,-2)(1,0,-2)} be a basis for a subspace of R^3 and let x=(-1,4,-2) be a vector in the…

A: The given basis vector are b1=0,2,-2, b2=1,0,-2. The given vector is x=-1,4,-2. (a) Therefore the…

Q: Find NS(A) of the given matrix A, for which n is NS(A) a subspace of R^n? Sketch NS(A) in R2 or R3.…

Q: Let W be the subspace of IR' spanned by the vectors 1 4 -2 and -1 -7 Find the matrix A of the…

Q: 3. Let P, be the vector space of polynomials of degree at most 2. Define a map D : P2 → P, it sends…

Question

Let T: R^3 --> R^3 be the linear transformation represented by the matrix in the image.

(a) Let ker(T)={v E R^3 | T(v) =0}, the kernel of the linear transformation. Give a description of ker(T).

(b) Show that ker(T) is a vector subspace of R^3.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given

VIEW

Step 2: Solution

VIEW

Step 3: Explanation

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find the orthogonal projection of v= [15 8 0] onto the subspace V of R^3 spanned by [-1 -2 -2] and [2 0 6]
There is no linear transformation T\colon \RR^5 \longrightarrow \RR^5 such that the range and kernel of T are the same subspace of \R^5. True/False ? Explain
Let A be any 5x7 matrix for which the col(A) has dimension 3, calculate: the nullity(A), and, state which vector space R^k that null(A) is a subspace of (give k). O A. nullity(A)=2, k=7 B. nullity(A)=4, k=7 OC. nullity(A)=2, k=5 O D. nullity(A)=4, k=5
If W\index{1} and W\index{2} are subspace of a vector space V(F), then show that W\index{1}+W\index{2} is also a subspace of V(F).
Define Vector Space and Vector subspace with the help of real time examples?
Let A be any 5x7 matrix for which the col(A) has dimension 3, calculate: the nullity(A), and, state which vector space R^k that null(A) is a subspace of (give k). A. nullity(A)=4, k=7 B. nullity(A)=2, k=5 C. nullity(A)=4, k=5 D. nullity(A)=2, k=7
choose:(true or false)
Let W be the subspace of IR' spanned by the vectors 3 and -6 12 Find the matrix A of the orthogonal projection onto W. A =
Find a basis for the two-dimensional subspace of R^4 defined by