if given the equation yi = B0 + B1xi +ui and express the same equation as y = xiB = ui (where xi and B here are vectors), does vector xi = [1 x1] or xi = [x1] (row vector) and B vector (column vector) = [B0; B1]?

Solve the following exercises, you will need to show all your work to receive full credit. Consider the matrix, 2 1 -2 2 3 -4 1 1 1 - Knowing that f(t) = (t – 1)²(t - 2) is the characteristic polynomial, do the following: 1. find a basis of eigenvectors; 2. Find P such that P- AP is a diagonal matrix D. Give D

デジタル形式で段階的に解決 ありがとう!! SOLVE STEP BY STEP IN DIGITAL FORMAT - Using the vectors A = 2xy + 3xzj - 2yk and B = 3xi-xyzj + 5xyk, answer the following questions: AxB={15x²yz-2xy²z}-{10x²y² +6xy}+{-2x²y²z-9x²z}k What is the cross product between "A" and "B"? What is the dot product between "A" and "B"? A.B=6x²y-3x²yz² - 10xy² Taking the value obtained in part a) of this problem, indicate what the value of the cross product of vectors "A" and "B" is at the point (3, 6, -1). Taking the value obtained in part b) of this problem, indicate what the value of the dot product of vectors "A" and "B" is at the point (-2, 0, -2). SOLVE THIS

The zero vector 0 = (0, 0, 0) can be written a linear combination of the vectors v., v,, and v- because 0 = Ov, + 0v, + 0v3. This is called the trivia! solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v., v,, and v- If not possible, enter IMPOSSIBLE.) V1 = (1, 0, 1), V2 = (-1, 1, 2), V3 = (0, 1, 6)

Determine the vector 8a – 7b if a = -3i + 2j – 4k and b = 5i + 6j + 2k. 8a – 7b = help (vectors)

3. If a = 3x - 5ỹ and b = -2x +9y, write the vector 5a-86 in terms of x and y

If vector u = 2-1+2:/ and vector V = 5-/+4), simplify each of the following, writing your final answer in the ai+ bj format of a vector. v-u= 2u-3v =

a, b and c are three vectors in the third dimension with the following properties: a × b does not equal zero. a × b = b × c = c × a. Show that a + b + c = 0. Show that a + b + c = 0.

Given the regression equation in 2 forms: (1) yi = B0 + B1xi + ui; (2) yi = xB + ui (where x and B in the 2nd equation are vectors). And both equations are the same. Does vector x = [1 x1] or [x1] (row vector)? Vector B = [B0; B1] (column vector)? Does

Loblolly is a built-in R dataset that that records the growth of Loblolly pine trees. We are interested in the height column of Loblolly. The values in the height column can be converted into a vector of name x by the assignment: x <- Loblolly$height We can see the values in x by typing x and Return or Enter. Remember x <- Loblolly$height After this assignment, we can see the first six values in x by typing head(x) and Return or Enter a. Give the R code to assign the values in in the height column of Loblolly to the vector named x. (Easy-see above) b. Calculate the interquartile range of x using the R, IQR() function. c. Calculate the sum of the squares of the values in x. d. Calculate the sample mean of x. e. Calculate the sample variance of x. f. Calculate the sample standard deviation of x. f. Using R, calculate a trimmed mean of x. [ h.Enter your R script in the box below.