Question

Let V = W = R2. Choose the basis B = {x1, x2} of V ,...

Let V = W = R2. Choose the basis B = {x1, x2} of V , where x1 = (2, 3), x2 = (4,−5) and choose the basis D = {y1,y2} of W, where y1 = (1,1), y2 = (−3,4). Find the matrix of the identity linear mapping I : V → W with respect to these bases.

Math   Algebra   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Let A =

1

-3

2

4

1

4

3

-5

The RREF of A is

1

0

17/7

1/7

0

1

1/7

-9/7

Hence (2,3) = (17/7)(1,1)+(1/7)(-3,4) and (4,-5) = (1/7)(1,1)-(9/7)(-3,4).

Let I: V →W be the identity linear mapping. Then I( x1) = I(2,3) = (2,3) = (17/7)(1,1)+(1/7)(-3,4) and I ( x2) = I(4,-5) = (4,-5)= (1/7)(1,1)-(9/7)(-3,4).

Thus, the matrix of the identity linear mapping I : V →W with respect to the bases B and D is M =

17/7

1/7

1/7

-9/7
0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
10 Linear Transformations. Let V = R2 and W = R3. Define T: V → W...
10 Linear Transformations. Let V = R2 and W = R3. Define T: V → W by T(x1, x2) = (x1 − x2, x1, x2). Find the matrix representation of T using the standard bases in both V and W 11 Let T :R3 →R3 be a linear transformation such that T(1, 0, 0) = (2, 4, −1), T(0, 1, 0) = (1, 3, −2), T(0, 0, 1) = (0, −2, 2). Compute T(−2, 4, −1).
Let S ∈ L(R2) be given by S(x1, x2) = (x1 +x2, x2) and let I...
Let S ∈ L(R2) be given by S(x1, x2) = (x1 +x2, x2) and let I ∈ L(R2) be the identity operator. Using the inner product defined in problem 1 for the standard basis and the dot product, compute <S, I>, || S ||, and || I || {Inner product in problem 1: Let W be an inner product space and v1, . . . , vn a basis of V. Show that <S, T> = <Sv1, T v1> +...
Let V=R2 with the standard scalar multiplication and nonstandard addition given as follows: (x1, y1)⊕(x2, y2)...
Let V=R2 with the standard scalar multiplication and nonstandard addition given as follows: (x1, y1)⊕(x2, y2) := (x1x2, y1+y2). Show that (V,⊕, .) is not a vector space.
Let V be Rn with a basis B={b1,...,bn}; let W be Rn with the standard basis,...
Let V be Rn with a basis B={b1,...,bn}; let W be Rn with the standard basis, denoted here by epsilon; and consider the identity transformation I : V --> W, where I(x) = x. Find the matrix for I relative to B and epsilon. What was this matrix called in Section 4.4?
Let X1 and X2 be independent random variables with joint pdf f(x1, x2) =x1e^−(x1+x2), 0< x1<∞,...
Let X1 and X2 be independent random variables with joint pdf f(x1, x2) =x1e^−(x1+x2), 0< x1<∞, 0< x2<∞. Y1= 2X1 and Y2=X2−X1. I) Find g(y1, y2), the joint pdf of Y1, Y2 Include and draw the support. II) Find g1(y1), the marginal pdf of Y1. III) Find E(Y1).
Let f(x1, x2) = 1 , 0 ≤ x1 ≤ 1 , 0 ≤ x2 ≤...
Let f(x1, x2) = 1 , 0 ≤ x1 ≤ 1 , 0 ≤ x2 ≤ 1 be the joint pdf of X1 and X2 . Y1 = X1 + X2 and Y2 = X2 . (a) E(Y1) . (b) Var(Y1) (c) Consider the marginal pdf of Y1 , g(y1) . What is value of g(y1) where y1 = 1/3 and y1 = 6/4 ?
Let W be an inner product space and v1,...,vn a basis of V. Show that〈S, T...
Let W be an inner product space and v1,...,vn a basis of V. Show that〈S, T 〉 = 〈Sv1, T v1〉 + . . . + 〈Svn, T vn〉 for S,T ∈ L(V,W) is an inner product on L(V,W). Let S ∈ L(R^2) be given by S(x1, x2) = (x1 + x2, x2) and let I ∈ L(R^2) be the identity operator. Using the inner product defined in problem 1 for the standard basis and the dot product, compute 〈S,...
Let X1 and X2 be a sample from a uniform distribution on [0, 1] and let...
Let X1 and X2 be a sample from a uniform distribution on [0, 1] and let Y1 = min{X1, X2}, Y2 = max{X1, X2}. Find fY1 (y1|Y2 = y2). A. 1/ 2 B. 1 / 2y2 C. 1 /y2 D. 2 E. 1
Let V be the subspace of all vectors in R 5 , such that x1 −...
Let V be the subspace of all vectors in R 5 , such that x1 − x4 = x2 − 5x5 = 3x3 + x4 (a) Find a matrix A with that space as its Null space; What is the rank of A? b) Find a basis B1 of V ; What is the dimension of V ? (c) Find a matrix D with V as its column space. What is the rank of D? To find the rank of...
Let A equal the 2x2 matrix: [1 -2] [2 -1] and let T=LA R2->R2. (Notice that...
Let A equal the 2x2 matrix: [1 -2] [2 -1] and let T=LA R2->R2. (Notice that this means T(x,y)=(x-2y,2x-y), and that the matrix representation of T with respect to the standard basis is A.) a. Find the matrix representation [T]BB where B={(1,1),(-1,1)} b. Find an invertible 2x2 matrix Q so that [T]B = Q-1AQ
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT