Consider the following matrix: A=[10 2] 013 Note that A is already in RREF. Our goal in this question is to describe the kernel % ker(A)={'JeR3 : AT}: 0} (a) We can write the equation A? = 0 more explicitly as: l; '3 fl 2 =l8l Write down the corresponding system of linear equations in variables x, y, z. {1 point) (b) Find the solution to this system of equations in vector form. Please show your work. (3 points) (c) Describe the set ker(A) as the span of some vectors, using part (b). (1 point) \"(A \\u puuua) Define a linear transformation T : R2 > R2 to be rotation by angle % clockwise about the origin. Remember that % radians is the same as 90 degrees. (a) What is the 2 x 2 matrix B corresponding to the linear transformation T? In other words, find the matrix B so that it?) = B?" for any vector i) E R2. (3 points) _> _) )- 0 . Are there any nonzero vectors 3) 75 0 such that T(?) = 0 ? Why or why > (b) Note that T( 0 ) = not? (2 points) Hint: You can use algebra to answer part (b), but alternatively you could think geometrically about how the function T transforms the vector 3