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(1 point) Find the matrix M of the linear transformation T:R? → Rgiven by - 1-5xı...
A Linear transformation T:R^5→R^4 is given as How do I find the standard matrix of T, the zero space and column-space of T? How do I find the rank and the dimension of the zero-space of T? C1 x2 1 as C2 + 4- x5 C4 C5
(1 point) If T:R? → R is a linear transformation such that -0-0-0-0-0-0) then
(1 point) If T:R → R is a linear transformation such that 13 , T||0||= 01) [ 1] T||1||= -1, Uo4 -4 i 2 1 T||0||= (11) then T|| -2
x 1.9.9 wuestion map Assume that Tis a linear transformation. Find the standard matrix of T. unchanged) and then reflects points through the line x2 + x4 T:R-R, first performs a horizontal shear that transforms e, into ez + 14, (leaving AO (Type an integer or simplified fraction for each matrix element.)
(1 point) Find the matrix A of the linear transformation from R to R given by -(:)-616) A=
Let T:R? → Rº be the linear transformation that first rotates points clockwise through 30° (7/6 radians) and then reflects points through the line y = 2. Find the standard matrix A for T. A=
(1 point) Find the matrix A of the linear transformation from R2 to Rºgiven by -6 -5 21 T 1 21+ 7 22 22 3 5 A=
Given real numbers a and b, find a linear transformation T:R^3→R^3 such that the range of T is the plane z=ax+by.
11.) Let T:R" - R"be a linear transformation. Prove T is onto if and only if T is one-to-one. 12.) Let T:R" - R" and S:R" - R" be linear transformations such that TSX=X for all x ER". Find an example such that ST(x))+x for some xER". - .-.n that tidul,
1. Is T a linear transformation? Justify completely a. T:R → RP defined by T(1, y, z) = (y, 1-22, y) b. T:R + P, defined by T(a,b,c) = (a - cr? - bx +1