Let T(x1, x2) = (-x1 + 3x2, x1 - x2) be a transformation. a) Show that...

Let T(x1, x2) = (-x1 + 3x2, x1 - x2) be a transformation.

a) Show that T is invertible.

b)Find T inverse.

Solutions

Expert Solution

Colby Messinger answered 11 months ago

Next > < Previous

Related Solutions

Let T: R2 -> R2 be a linear transformation defined by T(x1 , x2) = (x1...

Let T: R2 -> R2 be a linear transformation defined by T(x1 , x2) = (x1 + 2x2 , 2x1 + 4x2) a. Find the standard matrix of T. b. Find the ker(T) and nullity (T). c. Is T one-to-one? Explain.

consider the linear programming problem maximize z = x1 +x2 subjected tp x1 + 3x2 >=...

consider the linear programming problem maximize z = x1 +x2 subjected tp x1 + 3x2 >= 15 2x1 + x2 >= 10 x1 + 2x2 <=40 3x1 + x2 <= 60 x1 >= 0, x2>= 0 solve using the revised simplex method and comment on any special charateristics of the optimal soultion. sketch the feasible region for the problem as stated above and show on the figure the solutions at the various iterations

Show linear dependence or independence. Show all steps algebraically. a. let v1= < x1, x2, ......

Show linear dependence or independence. Show all steps algebraically. a. let v1= < x1, x2, ... , xn > and v2 = < y1, y2, ... , yn > be vectors in R^n with v1 not equal to 0. Prove that v1 and v2 are linearly dependent if and only if v1 is a non-zero multiple of v2. b. Suppose v1, v2, and v3, are linearly independent vectors in a vector space V. Show that w1, w2, w3, are linearly...

Let x0< x1< x2. Show that there is a unique polynomial P(x) of degree at most...

Let x0< x1< x2. Show that there is a unique polynomial P(x) of degree at most 3 such that P(xj) =f(xj) j= 0,1,2, and P′(x1) =f′(x1) Give an explicit formula for P(x). maybe this is a Hint using the Hermit Polynomial: P(x) = a0 +a1(x-x0)+a2(x-x0)^2+a3(x-x0)^2(x-x1)

Let X1 and X2 have the joint pdf f(x1,x2) = 2 0<x1<x2<1; 0. elsewhere (a) Find the...

Let X1 and X2 have the joint pdf f(x1,x2) = 2 0<x1<x2<1; 0. elsewhere (a) Find the conditional densities (pdf) of X1|X2 = x2 and X2|X1 = x1. (b) Find the conditional expectation and variance of X1|X2 = x2 and X2|X1 = x1. (c) Compare the probabilities P(0 < X1 < 1/2|X2 = 3/4) and P(0 < X1 < 1/2). (d) Suppose that Y = E(X2|X1). Verify that E(Y ) = E(X2), and that var(Y ) ≤ var(X2).

Let X1 and X2 be independent standard normal variables X1 ∼ N(0, 1) and X2 ∼...

Let X1 and X2 be independent standard normal variables X1 ∼ N(0, 1) and X2 ∼ N(0, 1). 1) Let Y1 = X12 + X12 and Y2 = X12− X22 . Find the joint p.d.f. of Y1 and Y2, and the marginal p.d.f. of Y1. Are Y1 and Y2 independent? 2) Let W = √X1X2/(X12 +X22) . Find the p.d.f. of W.

T::R2->R2, T(x1,x2) =(x-2y,2y-x). a) verify that this function is linear transformation. b)find the standard matrix for...

T::R2->R2, T(x1,x2) =(x-2y,2y-x). a) verify that this function is linear transformation. b)find the standard matrix for this linear transformation. Determine the ker(T) and the range(T). D) is this linear combo one to one? how about onto? what else could we possibly call it?

Let (Z, N, +, ·) be an ordered integral domain. Let {x1, x2, . . ....

Let (Z, N, +, ·) be an ordered integral domain. Let {x1, x2, . . . , xn} be a subset of Z. Prove there exists an i, 1 ≤ i ≤ n such that xi ≥ xj for all 1 ≤ j ≤ n. Prove that Z is an infinite set. (Remark: How do you tell if a set is infinite??)

The parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t...

The parametric equations x = x1 + (x2 − x1)t, y = y1 + (y2 − y1)t where 0 ≤ t ≤ 1 describe the line segment that joins the points P1(x1, y1) and P2(x2, y2). Use a graphing device to draw the triangle with vertices A(1, 1), B(4, 3), C(1, 6). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma-separated list of equations. Let x and y be in terms of t.)

let X1, X2, X3 be random variables that are defined as X1 = θ + ε1...

let X1, X2, X3 be random variables that are defined as X1 = θ + ε1 X2 = 2θ + ε2 X3 = 3θ + ε3 ε1, ε2, ε3 are independent and the mean and variance are the following random variable E(ε1) = E(ε2) = E(ε3) = 0 Var(ε1) = 4 Var(ε2) = 6 Var(ε3) = 8 What is the Best Linear Unbiased Estimator(BLUE) when estimating parameter θ from the three samples X1, X2, X3

Subjects