Define the linear transformation T by T(x) = Ax. Find ker(7), nullity(7), range(7), and rank(7). A = O|NO|AO|A |0|0|0 X

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Define The Linear Transformation T By T X Ax Find Ker 7 Nullity 7 Range 7 And Rank 7 A O No Ao A 0 0 0 X 1 (70.07 KiB) Viewed 11 times

Define the linear transformation T by T(x) = Ax. Find ker(7), nullity(7), range(7), and rank(7). A = O|NO|AO|A |0|0|0 X = D/HD/NON (a) ker(7) STEP 1: The kernel of T is given by the solution to the equation 7(x) = 0. Let x = (x₁, X2, X3) and find x such that T(x) = 0. (If there are an infinite number of solutions use t and s as your parameters.) STEP 2: Use your result from Step 1 to find the kernel of T. (If there are an infinite number of solutions use t and s as your parameters.) ker(T) = s, ter} 1 (b) nullity (T) STEP 3: Use the fact that nullity(7) = dim(ker(7)) to compute nullity(7). (c) range(T) STEP 4: Transpose A and find its equivalent reduced row-echelon form. 4 9 Na Na Ha STEP 5: Use your result from Step 4 to find the range of T. O -t, - -): t is real} OR O R² O {(t, -t, t): t is real} ○ {(t, -t, £): t is real} O (d) rank(T) STEP 6: Use the fact that rank(T) = dim(range(7)) to compute rank(7).