3. Let A E Rmxn (a) Show that yx = 0 for any x = N(A) and y = R(AT). (Hint: y = ZERm.) ATZ for some (b) Let x E Rn be such that y¹x = 0 for any y = R(AT). Show that x = N(A). (Hint: Choose y= AT Ax.)

Q: Q7 Assuming y = f(x), compute [3xy²] dx

A: The function is y=3xy2.To find : Compute ddx3xy2

Q: A. If z=x + f(u) and u=xy. Show that: x+y- ax =X

A: Question are not correct... I will send this type problem

Q: Let X-(1,0,-1,-V2)'. Then, |X|l2= Select one: a. 2 b. 1 C. 3

A:

Q: Exercise 2. Prove that dim(null T") = dim(null T) + dim W – dim V and dim(range T") = dim(range T),…

A: We prove dim null T*=dim null T + dim W-dim V and dim range T *=dim range T for every T L(V·W).

Q: g(x) = V4t + 5dt. Find g'(2). Let 3-x

A: We have given that  gx = ∫3-xx24t+5dt We have to find g'2 for that we have to use Leibniz integral…

Q: 2. Let f:Z→Z be the function given by fAn) =3n+1. a. Is fone-to-one? Briefly explain why. b. Is…

A:

Q: Find fry when 1. fxy 2. fxy 3. fxy 4. fxy f(x, y) = (x+2y)exy. = - (2 − xy)(x + 2y)exy (2 +…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Find fr and fy for f(x, y) = (1+2 – 2y)e"+2y 2y)e+2y

A: Given: - The function is, f(x,y)=(1+x-2y)ex+2y To find: - The value of fx and fy.

Q: B. Let H « G and K - G, and assume that HNK = {e}. Show that if x E H and y E K, then xy = yx

A: We can prove given result by definition of normal subgroup:

Q: es New Let x, = 1 ,x, = 2, f(1) = a, ƒ (2) = 2a, Q11(0.5) = 3. Then a = Select one: а. 7 b. 4 с. 6…

A: image is attached

Q: 1. Let x=(x) = (². Find xif 8. Exercise (2) ܘܚܢܟ b. x n

A: Given Data: Let us consider the given data, x=xn ∈l2. To Find: a. xn=212n b. xn=1n

Q: 1. Let f(x)=x² - x, xeR then f(f(f(v2))) is: -34 + V2. b. 2/2 +34. c. 34+2/2. d. 34– 2/2. e. 2/2 -…

A:

Q: Let f(x,y) = x - 4xy - y. Compute f(4,0) and f(4, – 4). f(4,0) = (Simplify your answer.)

A:

Q: Let w = f(x, y) with f E C² and x =h – kh, y = 4k. Which of the following statements are true?…

A: To find  Which of the given statement is true.

Q: F.T. 3) If X(t) + y(t) = x (2t - 1) =it W+1 Ans: Yow) = [4+jCW+1)]² X(w) and X (w.) = -j(w+1) e 2…

A:

Q: CALCULATE THE FOLLOWING USING MINOR COFACTOR AND COFACTOR EXPANSION 3 -8 2 A= 2 -6 3 4 4 2

A: A system of m×n numbers arranged in the form of a rectangular array having m rows and n columns is…

Q: 2. (6 pts) Let X = {1,2,3,4} and Y = {a,b,c} and define g: XY by specifying that g(1) = c, g(2) = a,…

A:

Q: Let f(x) = VT, 9(x) = ,. , andh(x) = x². (h o ((h o go f) – f)) (4) = %3D 5-x Select one: a. 4. 81…

A: let f(x) = x , g (x) = 45-x and h (x) = x2f (4) = 4= 2g (f(4) = g2= 45-2= 43h (g(f(4)) = h 43=…

Q: Let X have the pmf, Find the pmf of Y = X4. p(x) = (-)". 2 x= -1, -2, -3, ...

A:

Q: 41. For ), find all values ofx and y such thatx,y)=0 simultaneously. and yr.y)=0 f(x, y)…

A:

Q: 10. Let F(x, y, z)= y-yz+1 £z+r-z z+xy-y Find a function g such that F = √g.

A:

Q: 3. Let f (x) = x ² + 8x + 14. Find all the values interral C-G ,2) such that f (c) = 0 of ċ in the

A:

Q: Let Find fa, fay and fryz f(x, y) =In(xy)-26x¹0 y 10

A:

Q: Given, F = x²yî – 2xzj + 2yzk. Find V × (V × F)

A:

Q: 3.13. Let V D(0. 1). Suppose that f e C(V) NH(V), f(0) = 0 and |f(2)| < 1 for all z e V. Show that…

A: Given V=D(0,1) which is open disk with radius less than one. which is z&lt;1 Since f∈C(V¯)∩H(V)…

Q: Prove that for any x > 0, y>0 (x² + y²) ³ ≥ (x³ + y²³) ³. Hint: Introduce a new variable z = (2)².

A:

Q: let x be have P.dif 0 < x <3 f(x)= ={th find The U.b. of P(IX-M73) and find The L. b.

A: Please see below

Q: Let r = xi + yj + zk and r = |rl. If F = find div(F). (Enter your answer in terms of r and p.) p'…

A:

Q: 7. Given f(x) = x² – 5x ,

A:

Q: Q₂. if z=f(x+ct) + g(x-(t) then show that C²Z = Ztt XX

A: Given function: z=fx+ct+gx-ct We have to prove that, c2zxx=ztt. We know that, daxndx=anxn-1

Q: Z is the set of integers, R is the set of real mumbers. 1. Functions f, 9, and h are defined as f:R…

A:

Q: If f(x, y) = x²ye*xy, find fx and fyx.

A: Given function is

Q: Let f(x)= x+1, find all xeR such that f[f(x)]=2 the solution set is: а. у%3D0. b. y=x. с. у#х. d.…

A:

Q: 2. (8.7.10) Let f (x, y) In y R is the rectangle defined by R {(x, y)|1 < x < e2 and 1 < y < e}.…

A:

Q: Let f(x.y) = In (x³y) . If f(6,2)=f,(5,a) what is the value of a? O a 1 O b. -1 Oc. 0 Od. 2 O e. -2

A: