Question

23. [0/2 Points DETAILS PREVIOUS ANSWERS LARLINALGS 6.2.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Define the linear transformation T by Tx) - AX (a) Find the kernel of T. (If there are an infinite number of solutions use t as your parameter.) ker(- { -1,1,1,0 } (b) Find the range of T. <C-t, t): tis any real number) {(4): t is any real number) {(4, t): t is any real number) R? Need Help? Read Tutor 24. [0/2 points) DETAILS PREVIOUS ANSWERS LARLINALGS 6.2.017. ASK YOUR TEACHER PRACTICE ANOTHER Define the linear transformation T by Tv) - AX MY NOTES A- 312-1 (a) Find the kernel of T. (If there are an infinite number of solutions use t as your parameter.) kert? - { [-1,1,1,0] * } (b) Find the range of T. span{(1,0,0.-1), (0, 0, 1, -1)) span{(1, 0, 0, -1),(0,1,0,0) span{(1, 0, 0, -1), (0, 1, 0, 0, 0, 0, 1, -1) R OR Need Help? We

Answer 1

23(a) The linear transformation T in where given by T(X)=AX A= [ ì A Kert set of elements a for which A-0 holda. Now AXO 7 [o JE 20 * M-Ag+Anz=0 At Ango them and y=-8t. Let nyt At the kerT in RE 8+ At iter? - t 8 -A t being any real number Answer: 3 +1-8,-4,1) it is any real number

(6) Im(T) consists Ar. Now Anz po proible vectors of the form Thus [o 74] [7] - *[:]+na[i]+mg [] ametsa tam 3 [o], [1], [^] }. But [4] = 3 [o]+1. [i]. Hemce smety a stan} [i],[11] a linear transformation from dim (Im (T)) =2. Hence Im(T) = Last Answer: option in comect. R and