1,963 Answered Questions for the topic linear algebra

Linear Algebra

04/16/20

Representing a matrix in its "natural" space
Hi there,Any n*m matrix defines two vector spaces. The row space and the column space, and these both have the same dimensionality r, which is the rank of the matrix. Is there a way to represent... more
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Linear Algebra Algebra 1 Algebra

04/15/20

The linear transformation T:Rn→Rm is defined by T(v)=Av.Find:-
the dimensions of Rn and Rm. 1-A= ⌈ 0 1 -2 1⌉ -1 4 5 0 ⌊ 0 1 3 1⌋. 2-A= ⌈ 1 2 ⌉ -2 4 ⌊-2 2 ⌋.
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Linear Algebra Algebra 1 Algebra

04/15/20

Let T:R3→R3 be a linear transformation such that T(1,0,0)=(2,4,-1),T(0,1,0)=(1,3,-2),and T(0,0,1)=(0,-2,2) Find :-
1-T(0,3,-1)---------------------
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Linear Algebra Algebra 1 Algebra

04/15/20

Determine whether the fuction is a linear transformation(explain):-
1-T:R2→R2,T(x,y)=(x,1) 2-T:R3→R3,T(x,y,z)=(x+y,x-y,z)
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Linear Algebra Algebra 1 Algebra

04/15/20

use function to find (a) the image of v and (b) the preimage of w:-
1-T(v1,v2)=(v1+v2,v1-v2),v=(3,-14),w=(3,19) 2-T(v1,v2,v3)=(v2-v1,v1+v2,2v1),v=(2,3,0),w=(-11,-1,10)
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Linear Algebra Algebra 1 Algebra

04/15/20

The linear transformation T is defined by T(x)=Ax.Find (a) ker(T), (b) nullity(T), (c) range(T), (d) rank(T):-
A= ⌈ 4 1 ⌉ 0 0 ⌊ 2 -3⌋
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Linear Algebra Algebra 1 Algebra

04/15/20

The linear transformation T is represented by T(v)=Av.Find a basis for (a) the kernel of T and (b) the range of T:-
A= ⌈ 1 2⌉ ⌊ 3 4 ⌋
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Linear Algebra Algebra 1 Algebra

04/15/20

find the kernel of the linear transformation :-
1-T:R3→R3,T(x,y,z)=(0,0,0)2-T:R3→R3,T(x,y,z)=(x,0,z)3-T:R3→R3,T(x,y,z)=(z,y,x)4-T:R2→R2,T(x,y)=(x-y,y-x)
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Linear Algebra Algebra 1 Algebra

04/14/20

Whats the answer for these linear transformations questions?
Q1: use function to find (a) the image of v and (b) the preimage of w. 1-T(v1,v2)=(v1+v2,v1-v2),v=(3,-14),w=(3,19) 2-T(v1,v2,v3)=(v2-v1,v1+v2,2v1),v=(2,3,0),w=(-11,-1,10) Q2:determine whether the... more
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Linear Algebra Algebra 1 Algebra

04/14/20

Whats the answer for these karnel and range of a linear transformation questions?
Q1:find the kernel of the linear transformation. 1-T:R3→R3,T(x,y,z)=(0,0,0) 2-T:R3→R3,T(x,y,z)=(x,0,z) 3-T:R3→R3,T(x,y,z)=(z,y,x) 4-T:R2→R2,T(x,y)=(x-y,y-x) Q2:the linear transformation T is... more
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Linear Algebra

04/14/20

isomorphism and inverse

Let T : R2 → R2 be the linear transformation T(x, y) = (2y−x,3y−x) Compute the value of the inverseT-1 (3,3)=?
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Linear Algebra Algebra 1 Algebra

04/13/20

Whats the answer for these eigenvalues and eigenvectors questions?
Q1:verify that λi is an eigenvalue of A and xi is a corrcsponding eigenvector.1-A=⌈ 1 0 ⌉ ⌊ 0 -1⌋λ1 = 1, x1 = (1,0)λ2 =-1,x2 = (0,1)2-A=⌈ 4 -5 ⌉ ⌊ 2 -3 ⌋λ1 = -1, x1 = (1,1)λ2 =... more
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Linear Algebra Algebra 1 Algebra

04/13/20

Whats the answer for these karnel and range of a linear transformation questions?
Q1:find the kernel of the linear transformation.1-T:R3→R3,T(x,y,z)=(0,0,0)2-T:R3→R3,T(x,y,z)=(x,0,z)3-T:R3→R3,T(x,y,z)=(z,y,x)4-T:R2→R2,T(x,y)=(x-y,y-x)Q2:the linear transformation T is represented... more
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Linear Algebra Algebra 1 Algebra

04/13/20

Whats the answer for these linear transformations questions?
Q1: use function to find (a) the image of v and (b) the preimage of w.1-T(v1,v2)=(v1+v2,v1-v2),v=(3,-14),w=(3,19)2-T(v1,v2,v3)=(v2-v1,v1+v2,2v1),v=(2,3,0),w=(-11,-1,10)Q2:determine whether the... more
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Linear Algebra Algebra 1 Algebra 2 Algebra

04/12/20

graphing inverse
with the given points (4,2) (2,-1) (-2,-2) find the reflection of the original graph.
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Linear Algebra Calculus Geometry Algebra

04/10/20

Vector question.
Problem: A plane is set to head due east at 300 mph, but it is being pushed off course by a crosswind blowing south at 60mph. At 9AM the plane is located at point A(10,70)  and at 10AM the plane is... more
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Linear Algebra Geometry

04/08/20

Matrix diagonalizability
Consider the 4x4 matrixA = [1 2 4 0 0 -1 1 7 0 0 0 6 0 0 0 7]Is this matrix diagonalizable? Why or why not.
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Linear Algebra Math Calculus Geometry

04/08/20

Prove that T is a linear operator
Let T:R2→R2 be the function defined by T(〈x,y〉) = 〈-y,x〉.Hint: We want to show T(u + v) = T(u) + T(v) and T(λu) = λT(u) For all u,v ∈ R2 and λ ∈ R.
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Linear Algebra Math Algebra 1 Algebra 2

04/07/20

What kind of transformation converts the graph of f(x)=|x|+9 into the graph of g(x)=4|x|+9?
There is only one correct answer. The answer options are..Horizontal stretchvertical stretchhorizontal shrinkvertical shrinkits asking which one of these transformations/dilations makes the first... more
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Linear Algebra Math Algebra 1 Algebra 2

04/07/20

What kind of transformation converts the graph of f(x)=9x^2–9 into the graph of g(x)=x^2–1?
There is only one right answer.Here are the options...Vertical stretchvertical shrinkhorizontal stretchhorizontal shrink
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Linear Algebra Math Algebra 1 Algebra 2

04/07/20

What kind of transformation converts the graph of f(x)=|x|–1 into the graph of g(x)=8|x|–8?
The answer options are...horizontal shrinkhorizontal stretchvertical stretchvertical shrinkIts asking which one of these transformations above makes the first equation convert into the second one.
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Linear Algebra Algebra 1 Algebra

04/07/20

Whats the answer for these subspaces of vector spaces questions :
Q1:verify that W is subspace of V.In each caes,assume that V has the standard operations.1.W={(x1,x2,x3,0): x1,x2, and x3 are real numbers}V = R42.W={(x,y,2x-3y): x and y are real numbers}V = R33.W... more
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Linear Algebra

04/07/20

A copy machine makes 24 copies per minute how many copies does it make it four minutes and 45 seconds?
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Linear Algebra

04/07/20

A cab company charges $5 per cab ride, plus an additional $2 per mile driven. how long is a cab ride that costs $205?
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Linear Algebra

04/07/20

Whencompletinganonlineshoppingtransaction,atypicalshoppertakes14secondstoselecteachproductandanother20secondstocompletethecheck-outprocess.Howlongdoesittaketocompleteatransactionwith8products?
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