If T is defined by T(x)=Ax, find a vector x whose image under T is b, and determine whether x is unique. Let A - -4 11 [] b= Find a single vector x whose image under T is b. x=(2,1,0) 1 -5 -5 Wrea and

Let y 18 = = || -91 -3 and u 5 4 -2 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and 2 orthogonal to u. x₂ = ts ||

Suppose the vector x characterizing the antigenic state of an influenza virus population changes from one season to the next according to the equation 23 Xt + 1 ¹ -[3.39]** 0 0.9 If the vector in the current season is [...] what was the vector in the previous influenza season? ↓ 1

If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from a point P to the line L is equal to the length of the component of the vector AP that is orthogonal to the vector AB. L A Use the method above to find the distance from the point P(-3, 1,5) to the line through A(1,1,0) and B(-2,3, –4). NOTE: Enter the exact answer. Distance

Let U be a subspace of R", and let S = { ū, v, w } be a set of three non-zero vectors in R”. Fill in the blanks so that the following statements are true. If you believe you don't have enough information to conclude anything for any of the cases, choose the answer "???". Note that there is no intended relationship between the parts. In each case, assume only what the statement says to assume. If SCU, then dim(U) > (Enter the largest integer that makes the statement necessarily true.) If S is linearly independent and S C U, then dim(U) 3. If S' is a spanning set for U, then dim(U) 3. If span(S) = U then S If S is a basis for U, then S linearly independent. linearly independent.

what does the t mean t(1,1,1) vectors