Question 8 [10 points] Suppose T: RM22 is a linear transformation whose action on a basis for R4 ...
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...
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...
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...
Suppose T: R3–M2.2 is a linear transformation whose action on a basis for R3 is as follows: 0 -7 -7 -10 -10 T]01- T TI? 2 2 -7 -6 -10 -9 0 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 R3 Number of Vectors: 1 Bker...
Suppose T: M2,2-P2 is a linear transformation whose action on the standard basis for M2,2 is as follows: 1 0 0 1 0 0 0 0 T | = x2+x+2 = -x2+2x-3 x2–2x+4 T -2x2+x-4 0 0 o 0 1 Describe the action of T on a general matrix, using x as the variable for the polynomial and a, b, c, and d as constants. Use the '"' character to indicate an exponent, e.g. ax^2=bx+c. a b T = 0...
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:R4_R4 is the transformation given below. Determine whether T is one-to-one and/or onto. If it is not one-to-one, show this by providing two vectors that have the same image under T. If T is not onto, show this by providing a vector in R4 that is not in the range of T. 2x0+6x1+6x2+4x3 -2x0–x1-x2 + x3 |-3x0-8x1-5x2+4x3 xo+5x1+6x2+7x3 2 Tis one-to-one Tis onto
R4, and the set V of vectors i (4 points. Consider a linear transformation T: R3 in R3 such that T(T) = . Is V a subspace of R3? (8 points.) Suppose a matrix A is 6 x 4. Explain each of your answers in one sentence. If, looking at A, you can easily tell it has at least one row which is a linear com- bination of some of the other rows, what does that tell you about the...
need help on this. thanks in advance Question 16 Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 1-23 -1 3-4 2 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R. One-to-one; not onto #3 One-to-one; onto a Not one-to-one; onto R3 Not one-to-one; not onto a
Determine whether the linear transformation T is one-to-one and whether it maps as specified. Let T be the linear transformation whose standard matrix is 37 1 -2 A=-1 3 -4 -2 -9 Determine whether the linear transformation T is one-to-one and whether it maps R onto R O One-to-one; onto R O Not one-to-one: onto O Not one-to-one; not onto OOne-to-one: not onto