:(¤1, x2, . . . Xk)Let A be an p × k matrix, with columns a1, a2,be a vector in Rk. Give the definition of the product of A and x denoted by Ax inа...., ak. Let x =terms of the column picture. Explain to which space the product belongs to.b.Let23and B43 6A1 -51-2 3is the product AB defined? If so, compute it; if not explain why.

"Since you have asked multiple questions, we will solve the first question for you. If you want any…

Answered: a. Let A be an p × k matrix, with…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Determine if v is in the set spanned by the columns of B. B= 8-3 2 -9 4-7 6-2 4 5 -1 10 V= 12 -11 10 11 GETOP Choose the correct answer below and, if necessary, fill in the answer box(es) to complete your choice. OA. Vector v is not in the set spanned by the columns of B because the columns of B, b,, b₂, and b, are linearly independent. B. Vector v is not in the set spanned by the columns of B because the reduced echelon form of the matrix formed by writing B with a fourth column equal to v is OC. Vector v is in the set spanned by the columns of B because the columns of B span R¹. OD. Vector v is in the set spanned by the columns of B because b₁ b₂+ b3 FV. +
Please do last part
Problem 16 Let r(t) be a curve given by (3 sec 3t, 5 tan 3t, 1). Which of the following is the correct description of the curve in Cartesian coordinates. (i) x² + y² = 9, z = 1 rit1 = (3sec 3t 5 tan3t, 1) (ii) (iii) (iv) + sta za za Ans: (iii) 25 25 25 = = 1, z=1 = 1, z = 1 ||
Express each column vector of AA as a linear combination of the ordered column vectors C₁, C2, and c3 of A. -6 A = 6 2 4 3 Enter first column as a linear combination of columns of A in terms of the vectors C₁, C₂, and c3: Enter second column as a linear combination of columns of A in terms of the vectors C₁, C2, and c3: Enter third column as a linear combination of columns of A in terms of the vectors C₁, C₂, and c3:
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.
. Create a vector named prob18a that has 10 elements of which the first is 8, the increment is 7, and the last element is 71. Then, assign elements of prob18a to a new vector prob18b such that prob18b has 7 elements. The first 4 elements of prob18b are the first 4 elements of the vector prob18a and the last 3 elements of prob18b are the last 3 elements of prob18a. Do not type the vector elements explicitly.

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