Define T: R² → R³ by T() = A, where A = this transformation? -2 3. 1 -3. What is the image of u under 4 -3 -5

7. Consider the transformation w = 5x1- 3r, w =2x1+x2. Detemine whether the transformation is one-to-one.

Determine whether the following transformation from R3 to R? is linear.

Which rule describes the transformation b

Show that the transformation T defined by T(x1, X2) = (2x,- 3x,, x1 +4, 5x,) is not linear. %3D

4. Describe the transformations of y=-2f[3(x– 4)]–5.

Let T be a linear transformation from P₂ into P₂ such that T(1) = x, T(x) = 1 + x, and 7(x2) = 1 + x + x². Find 7(1 - 7x + 2x²). T(1 - 7x + 2x²) = Need Help? Read It Need Help? Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function. (Use C for the constant of integration.) Dx(f) = 8x + 6 Watch It Read It

Which of the following transformations are linear? yi X] + 10 y2 X2 8x1 Yı 7 y2 3x1 + x2 C. -Xi 0. y2 D. 9x2 %3D y2 E.3 y2 Уз 3 X1 7x1 – 2x2 + 6x3 y2 = 10x2 - 3x3 -4x1 – 9x2 F.- Y3 = |L || || || I| || || || IL || || || A. B.

.Define f: R- R by f(x) = rx + d, where r and d are real constants. Show that for f to be linear, it is required that d 0. (the definition of a linear transformation is given in text section 1.8) ()- 4r1-2 . Is the transformation T linear? YES or NO (circle one) I2 X122+3 Justify your answer:

A linear transformation T : R2 → R2first reflects points through the x1-axis andthen reflects points through the line x2 = −x1. Show that T can also be describedas a linear transformation that rotates points about the origin. What is the angleof that rotation?