Question

In: Math

Is the following map linear? a) F(x1,x2,x3)=(0,0) b) L:R2→R2 defined by L(x1,x2)=(3x1−2x2,x2) c) f:R→R defined by...

Is the following map linear?

a) F(x1,x2,x3)=(0,0)

b) L:R2→R2 defined by L(x1,x2)=(3x1−2x2,x2)

c) f:R→R defined by f(x)=2x

Solutions

Expert Solution

All the three maps are Linear here


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 system of equations below 3x1 − x2 + x3 = 1 3x1 +...
Consider the linear system of equations below 3x1 − x2 + x3 = 1 3x1 + 6x2 + 2x3 = 0 3x1 + 3x2 + 7x3 = 4 i. Use the Gauss-Jacobi iterative technique with x (0) = 0 to find approximate solution to the system above up to the third step ii. Use the Gauss-Seidel iterative technique with x (0) = 0 to find approximate solution to the third step
3. Given is the function f : Df → R with F(x1, x2, x3) = x...
3. Given is the function f : Df → R with F(x1, x2, x3) = x 2 1 + 2x 2 2 + x 3 3 + x1 x3 − x2 + x2 √ x3 . (a) Determine the gradient of function F at the point x 0 = (x 0 1 , x0 2 , x0 3 ) = (8, 2, 4). (b) Determine the directional derivative of function F at the point x 0 in the direction given...
Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if...
Let X1, X2, X3 be continuous random variables with joint pdf f(X1, X2, X3)= 2 if 1<X1<2 -1<X2<0 -X2-1<X3<0                         0 otherwise Find Cov(X2, X3)
Consider the following quadratic forms q(x1, x2) = 3x1^2 − 6x1x2 + 11x2^2 and r(x1, x2,...
Consider the following quadratic forms q(x1, x2) = 3x1^2 − 6x1x2 + 11x2^2 and r(x1, x2, x3) = x1^2 − x2^2+x3^2+ 2x1x2 − 6x1x3+2x2x3, on R 2 and R 3 , respectively. In both cases do the following. (a) Find the symmetric matrix A representing the quadratic form. (b) Find a corresponding orthogonal matrix P of eigenvectors of that matrix. (c) Write down the maximum and minimum values of the quadratic form over the unit vectors (in R 2 and...
Let X = ( X1, X2, X3, ,,,, Xn ) is iid, f(x, a, b) =...
Let X = ( X1, X2, X3, ,,,, Xn ) is iid, f(x, a, b) = 1/ab * (x/a)^{(1-b)/b} 0 <= x <= a ,,,,, b < 1 then, find a two dimensional sufficient statistic for (a, b)
Consider the linear system of equations 2x1 − 6x2 − x3 = −38 −3x1 − x2...
Consider the linear system of equations 2x1 − 6x2 − x3 = −38 −3x1 − x2 + 7x3 = −34 −8x1 + x2 − 2x3 = −20 With an initial guess x (0) = [0, 0, 0]T solve the system using Gauss-Seidel method.
Consider the TOYCO model given below: TOYCO Primal: max z=3x1+2x2+5x3 s.t. x1 + 2x2 + x3...
Consider the TOYCO model given below: TOYCO Primal: max z=3x1+2x2+5x3 s.t. x1 + 2x2 + x3 ? 430 (Operation 1) 3x1 + 2x3 ? 460 (Operation 2) x1 + 4x2 ? 420 (Opeartion 3 ) x1, x2, x3 ?0 Optimal tableau is given below: basic x1 x2 x3 x4 x5 x6 solution z 4 0 0 1 2 0 1350 x2 -1/4 1 0 1/2 -1/4 0 100 x3 3/2 0 1 0 1/2 0 230 x6 2 0 0...
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
1. Solve linear system using Gaussian elimination a) x1 + 2x2 + x3 = 2 -x1...
1. Solve linear system using Gaussian elimination a) x1 + 2x2 + x3 = 2 -x1 − 3x2 + 2x3 = -3   x1 − 6x2 + 3x3 = -6 b) -2b + 2c = 10 3a + 12b -3c = -6 6a + 18b + 0c = 19 c) 4x - 1y + 4z + 3t = 5 1x - 4z + 6t = 7 5x - 5y + 1z + 2t = -5 4x + 1y + 3z +...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT