Problems
For problem 9-15, determine
(a) Computing
(b) Direct calculation.
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Differential Equations and Linear Algebra (4th Edition)
- Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).arrow_forward(a) Let u and v be (fixed, but unknown) vectors in R". Suppose that T: R" → R" is a linear transformation such that T(u) = 6u + v and T(v) = 4u - 2v. Compute (T. T)(v), where TT is the composition of T with itself. Express your answer as a linear combination of u and v. (ToT)(v) = 10 u + -1 V Incorrect answer. Incorrect answer. (b) Let v and w be (fixed, but unknown) vectors in R", which are not scalar multiples of each others. Suppose that T: R" → R" is a linear transformation such that T(4v+3w) = -2v-2w and T(v+1w) = 5v+2w. Compute T(v) and express it as a linear combination of v and w. T(v) = 4 v + 2 W Incorrect answer. Incorrect answer.arrow_forward2. Now let W be the line y = 2x in R². (a) Find a unit vector u on W. (b) Consider the linear transformation T: R² → R² that projects each vector orthogonally onto W. Calculate the matrix for T as before. (c) Use that matrix to calculate T [4] -1 (d) Draw the vector [4] the line W, and the projection T[1] -1 -1arrow_forward
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