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- Consider a linear transformation T from R2 to R² for which (:) -}- T and T Find the matrix A of T. A =Let f be the invertible linear transformation represented by the matrix -2 ^-(-²¹) A = 1). 4 4 Find, in terms of and y, the equation of the image f(C) of the unit circle C. The equation isLet u = (1,1), v=(3,–2), w = (4,3), and y=(-3,4). Let L be a linear map from R² to R? such that L(u) =w and L(v) = y_ Find the transformation matrix L. If z = (3,5), what is 42) ?
- 3. Let vi - [1,-2,3], va -(-1,-4,5], and va [5,-1,3] be vectors in R'. a) Use determinant to show that vi. Va, and va are linearly dependent.10. Let (1,2,3) be a solution for the vector equation ru + yv + zw = 0 and consider the matrix A=[u,v,w] representing a linear transformation T. Pick the best option: a) NullSpace(T)={0} b) Range(T)={0} c) The list (u,v,w) is a basis for Nullspace(T) d) Dimension(Range(T)) < 3.Show that u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2) are linearly dependent show all working and explain clearl
- Calculate 121x dxdy where R is the parallelogram with vertices (0,0), (6,2), (7,6) R 1 -(v — Зи), у 11 -(4v – u) 11 and (1,4) using the transformation x =Consider B={1,x,x^2} and B'={1+x,1-x^2,2} Find the change of basis matrix 1.P from Bto B' 2.Q from B' to B Further find the relation between P and QConstruct a tollowingtronsformation single 2x2. matrix that defines the R A dilationof on factor 2, followed by a retlection in thesx-axis followed by a rotation trough "2. Fiad the inage of the point (,) under the transformatoons.
- u = (4,0,-2) and w = (2,1,6)Use cross productConsider the transformation T: R-R' given by T(x,X,X.a) = (x+8x. 0, 3x+XX,-x). Find the standard matrix representation for T and use it to determine if Tis one-to-one or outo. Justify your answers!! Paragraph BIU A 50 ...The dot product of two vectors in R³ is defined by - a¡b1 + a2b2 + azb3. _b3] a2 b2 аз 8. 9 Find the matrix A of the linear transformation from R³ to R given by T(7) = ủ · a. Let v = A