Suppose T: M2,2-P2 is a linear transformation whose action on the standard basis for M2,2 is...
Suppose T: P3-R is a linear transformation whose action on a basis for Pa is as follows 45 0 -3 0 0 T(-2x-2) T(-2x3-2x2-2x-2) T(x3+2x2+2x+2) = 12 T(1) 1 4 -13 |-2 -3 2 Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two polynomials that have the same image under T If T is not onto, show this by providing a vector in R that is not in the image of T...
Suppose T: M2,2 P2 is a linear transformation whose action is defined by s and that we have the ordered bases 1 00 1 0 000 0 00 010 0 1 D-1x2 for M2.2 and P2 respectively. a) Find the matrix of T corresponding to the ordered bases B and D MD(T) 0 0 0 b) Use this matrix to determine whether T is one-to-one or onto < Select an answer >, < Select an answer >
Suppose T: M22-R3 is a linear transformation whose action on a basis for M2.2 is as follows: 6 1 -3 -3 0 1 1 1 T T T T -3 -3 0 1 1 2 1 Give a basis for the kernel of T and the image of T by choosing which of the original vector spaces each is a subset of, and then giving a set of appropriate vectors. Basis of Kernel is a Subset of M2,2 Number of...
Urgent please,thanks Suppose T: P3R4 is an isomorphism whose action is defined by -2a+d 2b+c Tax3 +bx+cx+d) = -2a+2d c+d Find the inverse transformation T-1 and give its action on a general vector, using x as the variable for the polynomial and p, q, r, and s as constants. Use the " character to indicate an exponent, e.g. px^2-qx+r.
Question 1 [10 points] Suppose T: M2.2-R3 is a linear transformation whose action on a basis for M2,2 is as follows: Give a basis for the kernel of T and the image of T by choosing which of the original vector spaces each is a subset of, and then giving a set of appropriate vectors. Basis of Kernel is a Subset of M22 Number of Matrices: 1 Bier = {0} Basis of Image is a Subset of M2.2 Number of...
Let T: P2 + P, be a linear transformation for which T(1) = 3 - 2x, 7(x) = 9x – x2, and 7(x2) = 2 + 2x2. Find T(2 + x - 8x?) and T(a + bx + cx?). T(2 + x - 8x2) T(a + bx + cx) II
Question 8 [10 points] Suppose T: RM22 is a linear transformation whose action on a basis for R4 is as follows -1 1 -11 4 4 0 1 1 0 1 -1 1 -45 1 2-2 1 -1 7 0 Determine whether T is one-to-one andlor onto. If it is not one-to-one, show this by providing two vectors that have the same image under T. If T is yt onto, show this by providing a matrix in M22 that is...
Let T:P1→P2T:P1→P2 be a linear transformation defined by T(a+bx)=3a−2bx+(a+b)x2.T(a+bx)=3a−2bx+(a+b)x2. (a) Find range(T)range(T) and give a basis for range(T)range(T). (b) Find ker(T)ker(T) and give a basis for ker(T)ker(T). (c) By justifying your answer determine whether TT is onto. (d) By justifying your answer determine whether TT is one-to-one. (e) Find [T(7+x)]B[T(7+x)]B, where B={−1,−2x,4x2}B={−1,−2x,4x2}.
Let T:P1→P2 be a linear transformation defined by T(a+bx)=3a−2bx+(a+b)x2. (a) Find range(T) and give a basis for range(T). (b) Find ker(T) and give a basis for ker(T) (c) By justifying your answer determine whether T is onto. (d) By justifying your answer determine whether T is one-to-one. (e) Find [T(7+x)]B, where B={−1,−2x,4x2} Please solve it in very detail, and make sure it is correct.
Let T:ℙ2(ℝ)→ℙ2(ℝ) be a linear transformation given by T(f(x))=3f′(x)+9f(x). If TS:ℝ3→ℝ3 is the corresponding coordinate transformation with respect to the standard basis for P2, {1,x,x2}, compute the matrix AS of the coordinate transformation. (Hint: Consider how T transforms an arbitrary polynomial of the form f(x)=a+bx+cx2.) AS= ⎡⎣⎢⎢⎢⎢⎢ ⎤⎦⎥⎥⎥⎥⎥