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- Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find T(7,2).Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).1. Is L = {1 − 2x + 3x^2, x − 2x^2, 2 − 5x + 8x^2} linearly independent? If yes, show why. If not, show a dependence relationship. Is L = {1 + 2x + 2x^2, x − 2x^2, −2 − 3x − 5x^2} linearly independent? If yes, show why. If not, show a dependence relationship.
- Each of J, K, L, M and N is a linear transformation from R2 to R². These functions are given as follows: Jx1, х2) %3D (Зхі — 5х2, —6х1 + 10x), K(x1, x2) = (-V3x2, 3x1), L(x1, x2) = (x2, –x1), M(x1, x2) = (Зх1 + 5х, бх1 — бх2), N(x1, x2) = (-v5x1, v5x2). (a) In each case, compute the determinant of the transformation. . det J= ,det K ,det L= ,det M= ,det NFind the Wronskian and determine whether the given set of functions is linearly independent on the interval (-∞, ∞)If f(x) = x* + 3, g(x) = x – 9 and h(x) = Væ, then f(g(h(x)))= MacBook Pro esc G Search or type URL @ 23 $ & 1 2 3 4 5 6 8 9 Q W E R Y U A S F G H K V N motion command comman B
- Suppose a firm's technology is represented by the production function f(L, K) = min(L, 2K), where L is the quantity of labor and K is the quantity of capital. Consider the isoquant through input combination (L, K) = (4, 8). Which of the following statements is true? The isoquant through input combination (L, K) = (4, 8) has a corner at A input combination (L, K) = (4, 8). The isoquant through input combination (L, K) = (4, 8) has a corner at input combination (L, K) = (4, 2). %3D %3D The isoquant through input combination (L, K) = (4, 8) has a corner at C input combination (L, K) = (8, 8). The isoquant through input combination (L, K) = (4, 8) has a corner at input combination (L, K) = (8, 4).6. Show that T is a linear transformation. T(x1, x2) = (2x2 – 3x1, x1 4x2, 0, x₂).Let the utility function be U=f(q1,q2) subject to budjet constraint M=p1q1 +p2q2 derive the slutsky equation (dq1/dp1) to show Price effects (substitution and income) and illustrate The effects with the help of graph.