# 25. (-/23 Points] DETAILS LARLINALG8 6.1.501.XP.SBS. The linear transformation T: R RM is defined by…

25. (-/23 Points] DETAILS LARLINALG8 6.1.501.XP.SBS. The linear transformation T: R RM is defined by Tv) = Av, where A is as follows. 0 1 -6 1 -1 7 40 0 1 9 1 (a) Find T(0, 3, 2, 1). STEP 1: Use the definition of T to write a matrix equation for TO, 3, 2, 1). T10, 3, 2, 1) = and STEP 2: Use your result from Step 1 to solve for T(0, 3, 2, 1). Ti0, 3, 2, 1) = 1 100 (b) Find the preimage of (0, 0, 0). STEP 1: The preimage of (0, 0, 0) is determined by solving the following equation. 0 1 -6 1 Tw, x, y, z) = -1 7 40 0 1 9 1 y 0 Lett be any real number. Set z = t and solve for w, x, and y in terms of t. W = z = STEP 2: Use your result from Step 1 to find the preimage of (0, 0, 0). (Enter each vector as a comma-separated list of its components.) The preimage is given by the set of vectors {( ): t is any real number). Need Help? Read it Talk to a Tutor Submit Answer 26. [0/1 Points) DETAILS PREVIOUS ANSWERS LARLINALG8 6.2.001. Find the kernel of the linear transformation. (If all real numbers are solutions, enter REALS.) T; R = R2, Tx, y) = (0, 0) ker(7) = { (xy) :X, Y CRY YER} X Need Help? Read it Watch It Talk to a Tutor

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