Mathematics
Mathematics, 05.07.2019 00:10, heatherballiet866

Part ii: let l: r-> r2 be the linear transformation defined by l u find ker l hint: to find the ker l, we must determine all v in r3 so that l (v) =0 r2 (0 is the zero vector)

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Mathematics, 12.07.2019 19:30, thelordoftheknowwjo4
0-3 -2 1 5. let t(x) ax, where a b = -3 1 6 3 2 -2-1 find vector x whose image under t is b. determine whether x is unique. 1 -3 5-5 -1 let t(x) ax, where a , is b= in the range of t? 6. 0 5 1 -3 1 = -4 0 2 4-4 why or why not? -1-2 -l- transformation that maps x into x1v1+x2v2. find matrix of a such that tx ax for each x. r2 be a linear 7. let e and v and, let t: r2 = 8. show that t(x1,x2, x3) = (x1 -5x2 +4x3,x2-6x3) is a linear transformation by writing as a matrix máltiplication. find images under t of u v and 2u +3v, where u = t(x) -2 21 and v= 1 9. for what value (s) of k will the product ab ba if a and b 3 4 -1 -l31 4 compute the matrix ab. show that (ab)t = btat 10. if a= 2 and b -3
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Mathematics, 17.07.2019 19:10, whismanjames
3. consider the transformation, t: p1 p2 defined by tax +b) = ax^2 + ax +a (a) show that t is a linear transformation. (b) find the image of 2.0 +1. (c) find another element of p, that has the same image. (d) is t a one-to-one transformation? why or why not? (e) find ker(t) and determine the basis for ker(t). what is the dimension of kernel(t)? (f) find range(t) and determine a basis for range(t). what is the dimension of range(t)?
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Mathematics, 20.07.2019 01:20, Teephat
Let l: r^rightarrow r^3 be a transformation defined by l[(u_1, u_2, u_3, u_4)^t] = (u_1 + u_2, u_3 + u_4, u_1 + u_3)^t. [7 p] (a) show that l is a linear transformation. [9 b] (b) find a basis for kernel of l, ker(l), and determine its dimension. [9 p] (c) find a basis for image of r^4, l(r^4), and determine its dimension.
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