Each of J, K, L, M and N is a linear transformation from R2 to R². These functions are given as follows: Jx1, х2) %3D (Зхі — 5х2, —6х1 + 10x), K(x1, x2) = (-V3x2, 3x1), L(x1, x2) = (x2, –x1), M(x1, x2) = (Зх1 + 5х, бх1 — бх2), N(x1, x2) = (-v5x1, v5x2). (a) In each case, compute the determinant of the transformation. . det J= ,det K ,det L= ,det M= ,det N

3- (a) u=- 4 +31 +3, v=+2 + 4t-1, w = 21 -- 31+5; (b) u=- S - 21 + 3, v-4 - 31 + 4, w= 2r - 17 - 71 +9. Determine whether the following polynomials u, v, w in P(1) are linearly dependent or independent:

Create 2 sets, one linearly independent and one linearly dependent, by replacing the x with a number, starting from B = { (1,2,-1,8), (-2,-1,4,2), (13,14,-21,x) }

Let y = U 4 + 5 U and u = = = x³ - 2x.

Is {(3, 4)}Linear combination of {(1,2), (2, 4)} show all the work and state why why not. or

6. Which of the following four functions is (are) linear functions? Function A: y =x - 2 Function B: y= 2* Function C: Function D: y =4x3 Choose: O All four are linear functions. OFunction B and D are linear. O Only function D is a linear function. O None of the four are linear functions. Which of the following equations represent non-linear efine y in terms of x? 70ose all that apply. Then hit "Submit". ソ=4x2

A group sells bird feeders to raise money. The group sells an average of 10 feeders per week at a price of $35 per feeder. The group conducts a survey and finds for every five dollar increase in price, it will lose two sales per week.  A) What is the demand function for the bird feeders, that is, what is the average quantitiy q of the feeders sold as a function of price p per feeder? B) find a function that models the revenue R in terms of price p per feeder. C) What price should be charged to maximize the revenue?  D) What would the mximun revenue be at that price?

Problem YOUDEN RECTANGLE'S PROBLEM BIBD- Balanced Incomplete Block Design . There is a matrix m x n. This matrix can be 26 x 4 but we can change this dimension if 26 x 4 does not admit a feasible solution. • m> n + 1 • The rows are called "blocks" and the columns are called "forms" • Every form is composed by the same number of blocks • • Every block is composed by the same number of forms The matrix is full and every single spot should be filled with a treatment Every treatment is is replicated r times in the Youden rectangle • Every treatment appears in every form maximum one time • Every couple of treatment appear together in every form 1 times Every treatment appear in all single blocks the same number of times v = number of treatments (1,2,3,4,.....,n) n = blocks (columns) m = forms (rows) r = number of times every treatment is replicated λ = number of times two treatment appear together in the same form Constraints: 1) nxm=vxr - 2) 1 (v 1) = r (k-1) 3) m > v then r > n Goal The…

Which of the following is true regarding the function y = ax 4 + bx² + c? The function only has exactly one critical point if a and b have same signs. The function only has exactly one critical point if a and b have different signs. The function has exactly two critical points all throughout its domain for any value of a and b. The function has exactly three critical points all throughout its domain for any value of and The function has exactly one critical point all throughout its domain for any value of and.