Let 7= A = Is the vector unique? choose 4 3 6 -11 2 -6 4 -5 2 57 -25 Define the linear transformation T: R³ → R¹ by T(z) = Az. Find a vector a whose image under Tis 6. 5 and b = -397 -14 -39 226

Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).

Let T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.

Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a the kernel of T and b the range of T. c Determine the rank and nullity of T.

Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set {v12v2,2v23v3,3v3v1} linearly dependent or linearly independent? Explain.

Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors {vu,wv,uw} is linearly independent or linearly dependent.

Let I represent the identity transformation that does nothing to a vector. I: (-5,1)→ I can be represented by the matrix

Let A = 10-3 -3 16 2-2 -1 -2 3 1 Consider the transformation T defined by T(x)=Ax. Find a vector x whose image under T is vector b. Analyze whether x is unique. Describe the arguments on which you base your answers.

Let A = X = - -5 -5 -6 Is the vector x unique? choose 4 6 2 -3 4 -41 5 Define the linear transformation T: R³ → R¹ by T(x) b. and b = = 58 29 3 72 Ax. Find a vector x whose image under Tis

Assume that T is a linear transformation. T: Projects vectors in its domain onto the line y = 2/3 x. Find the standard matrix of T. Enter your matrix as 4-tuple (a11, 12, 921, 922) Use only fractions in simplest form and integers. NO DECIMALS "a11 11 "),a12= ,a21= ,a22=