Don't use chat gpt It (3). Define a linear transformation T: R2 R2 by→>where G =cos (0) - sin(0)cos(0) cos(0)3) ₁ 0 <0<satisfies the equation A² - (a + d) A+ (ad - bc)I = 0, for any real numbersT(x) = Gx-x,a b0. Then linear transformation T is one-to-one and onto. ( )(4). The matrix A =C da, b,c and d, where O denotes a 2 x 2 square matrix.distinot piconvalues then so does 4².

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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Let x=x(t) be a twice-differentiable function and consider the second order differential equation x+ax+bx=0(11) Show that the change of variables y = x' and z = x allows Equation (11) to be written as a system of two linear differential equations in y and z. Show that the characteristic equation of the system in part (a) is 2+a+b=0.
Q.4. Let T is a transformation from R' into R’ defined by: T(x,x, , x; ) = (2x, –x;, 2x; – 4x,, x, – 5x, – 2x, ). - - (a) Is T a linear transformation? Justify your answer. (b) Show that T is invertible. (c) Find a formula for T.
Is the following a linear transformation?
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Q1. Decide which of the following functions are linear transformation? (i). T : R² → R² defined as, T(x, y) = (y, x + 1). (ii). T : M22 → R defined as, T(A) = a + b+c+ d. Thope for a clear solution (iii). T : R² → R³ defined as, T(x, y) = (x + y, x + 1, 3y). (iv). T : R² → R³ defined as, T(x, y) = (/x, xy, V9). (v). T : M22 → M22 defined as, T(A) = A¬!.
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. Define a linear transformation T: R² → R² by ere G = 3)₁0<0< cos (0) -sin(0) cos(0) cos(0) T(x) = Gx-x, <<. Then linear transformation T is one-to-one and onto.