Given the elow bases for R^2 and the point at the specified coordinate in the standard basis as below, (40 points)

Wribreeminsl 2020-10-18 Answered

Given the elow bases for R2 and the point at the specified coordinate in the standard basis as below, (40 points)

(B1={(1,0),(0,1)}&

B2=(1,2),(2,1)}(1, 7) = 3(1,2)(2,1)
B2=(1,1),(1,1)(3,7=5(1,1)+2(1,1)
B2=(1,2),(2,1)   (0,3)=2(1,2)2(2,1)
(8,10)=4(1,2)+2(2,1)
B2 = (1, 2), (-2, 1) (0, 5) =
(1, 7) =

a. Use graph technique to find the coordinate in the second basis. (10 points) b. Show that each basis is orthogonal. (5 points) c. Determine if each basis is normal. (5 points) d. Find the transition matrix from the standard basis to the alternate basis. (15 points)

 

You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

lamusesamuset
Answered 2020-10-19 Author has 93 answers

B1={(1,0)(0,1)} standard basis R2 Alternate basis B2={(1,2)(2,1)},B2={(1,1),(1,1)}B2={(1,2)(2,1)},andB2{(1,2)(2,1)}) a. (0,5)=a(1,2)+b(2,1)=(a2b,2a+b)
a2b=0 and 2a + b = 5
a=2b7b+b=55b=5b=1thena=2,
(0,5)=1(1,2)+2(2,1)(1,7)=(1,2)+b(2,1)=(a2b,2a+b)a2b=1 and 2a+b=7
2aab=25b=5b=1a=3(1,7)=3(1,2)+1(2,1)
b. B2={(1,2)(2,1)} is orthogonal since [12][21]=22=0
B2={(1,1)(1,1)}
is orthogonal since ([11][11])=11=0B2={(1,2)(2,1)} is not orthogonal since [12][21]=2+2=70.B2={(1,2)(2,1)}is orthogonal c. The vector UR2 is normal of null=1B at every vector in B2 is not normal. They are unit vectors X All bases B2 are not normal X. d. The transition matrix from B to BisTB2B=[[b1]B2[b2]B2]
b1=[10],b2=[01],B={b1,b2}
standard basis B2={(1,2)(2,1)}Then (10)=a(12)+b(21)=(10)=(a+2b2ab)a=15b=25
Therefore

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2020-12-02
As you can see the solution to the system is the coordinates of the point where the two lines intersect. So, when solving linear systems with two variables we are really asking where the two lineas will intersect.
asked 2021-03-02
To plot: Thepoints which has polar coordinate (2,7π4) also two alternaitve sets for the same.
asked 2020-12-30
Let A := 5 1 16 -3 [2 3 9 4 (a) Find a basis for Nul A. (b) Find a basis for Col A.
asked 2020-11-22
True or False? In Exercises 99 and 100, determine whether the statement is true or false. Justify your answer, : 99. The line through (−8,2) and (−1,4) and the line through (0,−4) and (−7,7) are parallel.
asked 2022-04-19

[ k 1 −2 ,4 −1 2]

asked 2020-11-01

Give a full correct answer for given question 1- Let W be the set of all polynomials a+bt+ct2P2 such that a+b+c=0 Show that W is a subspace of P2, find a basis for W, and then find dim(W) 2 - Find two different bases of R2 so that the coordinates of b=[53] are both (2,1) in the coordinate system defined by these two bases

asked 2021-01-30

A line L through the origin in R3 can be represented by parametric equations of the form x = at, y = bt, and z = ct. Use these equations to show that L is a subspase of RR3  by showing that if v1=(x1,y1,z1) and v2=(x2,y2,z2)  are points on L and k is any real number, then kv1 and v1+v2  are also points on L.