2 Given t = -1 and U = -1|, for which is the set {u, T, w} {d, v, 2 linearly independent?

Q: For which value(s) of s, if any, v1, Let Vi V3 S 1 V2 and v3 are linearly independent.

A: For linearly independent, mode of matrix of vector is zero.

Q: Suppose that T : R2 --> R2 is linear, T(1,0) = (1, 4), and T(1, 1) = (2, 5). What is T(2, 3)? Is…

A:

Q: Find the nullity of T.T: R4→R2, rank(T) = 2

A:

Q: ди ди ди for u = az Find p-q if p= x+ y+ z ,q = x + y + z ,r = = (V3,2,1). and ax' əy 9-r x + y - z…

A: Q3. Given that                                            u=p-qq-rp=x+y+zq=x+y+zr=x+y-zPoint, (x, y,…

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = √(x2 + y2 +…

A: Given: Function f(x,y,z) as follows: and a point (1,2,2) To find: Linearization L(x,y,z) of the…

Q: If |r(t)| = c (a constant), then r' (t) is orthogonal to r(t) for all t.

A:

Q: Suppose v, w e R" and {v, w} is linearly independent. Prove that {v – w, 2v+w} is linearly…

A:

Q: S(x)dt, iff(x)= Vx-k+1;k-13x< i, k=1, 2.n.

A: By substitution, we calculate the following Integral.

Q: The functions y1, Y2, . .. , Yn are linearly independent, if and only if W (y1, 32, ..., Yn)(to) #0…

A: If two functions are linearly dependent then the Wronskian is zero for every value of t.

Q: If (x, y, z) = x²yz³ and A = xzi -y²j + 2x²yk, Determine : ww a) Ax (Vx A) at point (1,-1,1) b) VX…

A:

Q: Find the EXACT Jacobian a(x,y) d(u, v) 1 1 - -— (9u - 4v), y = —— (3u +3v) 4 4 X = for the following…

A:

Q: Suppose b, c E R. Define T: R³ → R² by T(x, y, z) = (2x − 4y + 3z + b, 6x + cxyz). Show that T is…

A:

Q: The set of functions {Vx, x, x²} is linearly dependent on (0, oo). True False

A:

Q: o Find the Vf at the given point 1.f (x,y,2)=x² + y² -2:2 +z In x,P(1,1,1)

A:

Q: дz For z = x² + xy³ ; x = uv² + w², y = u + vew, find when u = 2, v = 1, and w=0 Əw

A: z=x2xy3, x=uv2+w2, y=u+ve2at u=2, v=1 and w=0, x=2×12+0=2y=2+1e0=2

Q: = In z are two linearly indepen- of ry" + y' = 0, then the partic- - ry" + y' = f(x) can be written…

A: We have to choose the correct answer from the given options according to the given condition

Q: 4) Suppose that T : R³ → R² is defined by T((x, y, z)) = (1+2x – z , 3 – x + 6y) Is T linear?…

A:

Q: The functions y1, Y2, . .. , Yn are linearly independent, if and only if W (y1, Y2, ..., Yn)(to) # 0…

A: We can use the Wronskian test to check the functions are linearly independent or dependent.

Q: 3. Show that S4 has the presentation (x, y|x* = y² = (xy) = 1). %3D

A: To show: S4 has the presentation x,y| x4=y2=(xy)3=1

Q: Find f, and f and evaluate each at the given point. 2xy x, - V+ ay (1, 1) K, ) - Sx, ) - (1, 1) - 29…

A: The solution of the problem is given in the next steps.

Q: Consider x1 = et and x2 = v(t)et. If x1 and x2 is linearly independent, then v′(t) = 0. Is this…

A:

Q: (a) Vx E R, 3y E Z such that y > x + 110. (b) Vx E Z, 3y E N such that y > x + 110. (c) 3x E Z such…

A:

Q: 13. Let f(x, y, z) = xy+z², with x(s,t) = s², y(s, t) = 2st, and z(s, af/ds and df/dt %3D %3D

A:

Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by fX,Y (x, y) = x + y/21…

A: Solution

Q: 1 if i= j 0 otherwise. P:(c;) = 5 is a linearly independent set.

A:

Q: Suppose v1, ..., Vm is linearly independent in V and w e V. Prove that if vi + w, ..., Vm +w is…

A:

Q: Given z=x^3+xy^2,  x=uv^3+w^2,   y=u+ve^w then find: ∂z/∂u when u=−1, v=−2, w=0u=-1, v=-2, w=0

A:

Q: Suppose T: R3 M33 is a linear defined by T (x, y, z) = I 2y 0. Then ker(T) is OA. { (0, 0, 0) } Ов.…

A:

Q: 1- If z = 1+ y2, we can write: a) z = 1- (iy)?, b) z = 1- iy?, c) z = 1- iy, d) z 1 + (iy)? 2- If z,…

A: As you have posted multiple questions so according to our guidelines, I answered first three…

Q: ction W, then {po, P₁, Pn} is a linearly independent set. for Chebyshev polynomials 0, n‡m, (Tn, Tm)…

A: Note: since you have posted multiple questions. As per our guidelines we have to solve only one…

Q: 2. Find Df(x, y, z) for f(r, y, z) =x In z+r+ y at (0,0, 2).

A:

Q: Consider the Simple Linear Model: 4 = Bo + Biz, + e, where i = 1,...,n, and e ~ IID(0, o?). Suppose…

A: Simple linear regression model: A simple linear regression model is given as y = b0 + bx, where y is…

Q: M1 := sup ||T(x)|| and ||x||=1 M2 := inf{C > 0 : ||T(x)|| < C||x|| for all x e R"}. a) Prove that M1…

A:

Q: 5) Find ôw/ôv if w=x² +(y/x), x u-2v+1, and y= 2u +v-2, at the point (u, v) = (0,0)

A: We have to find all partial derivatives first.

Q: (b) Let h(x, y, z) = x?y+ yz?, where a = u + v, y = u – v and z = -u. Calculate and ди dv

A:

Q: Let r E R and --(), v- (), -- (1). 3 u = V = W = 2 For which values r ER is the set {u, v, w}…

A:

Q: Consider ф: C" — C defined by ф(x) %3D х*. a) Kerф %3D (1,-1} b) Kerø = {i,-i} %3D с) Kerф %3D (1,1}…

A:

Q: The functions y1, Y2, · . . , Yn are linearly independent, if and only if W (y1, 22, *. Yn) (to) # 0…

A: Consider the following differential equation, y''+pxy'+qxy=0

Q: If r(t) = (V10 – t, In(t – 1) - then the domain of r is

A: Domain = (1, 10]

Q: b) Suppose to i that and V х-у Calculate the x and and y by and Jacobian ð (u, v) 2 (x, y) hence…

A: Suppose that x and y are related to u and v by…

Q: Assume that z = ƒ(w), w = g(x, y), x = 2r^3 - s2, and y = re^s. If g x(2, 1) = -3, g y(2, 1) = 2,…

A:

Q: If w = e" + v², z = u³v+ 2ve", u = x2 - y?, v = 3/xy Find a(w.z) a(x.y) at p(1,1)

A:

Q: S_f(x.y,z)ds

A: The solution is given as

Q: In C[0, 1], are the functions {x2 , x3 , e2x} linearly independent?

A: Linearly dependent and independent functions: Two differential functions f(x) and g(x) are said to…

Q: Suppose that T: R2→ R2 is linear, T(1, 0) = (1, 4), and T(1, 1) = (2, 5). What is T(2,3)? Is T…

A: Given,

Q: If F(x,y, z) = (5x – y + az)î + (bx + 2y + 5z)ĵ + (2x + cy – z)k is irrotational then find the value…

A: Explanation of the answer is as follows

Q: Let ƒ (x, y) = x² - y² . Find all all points (x, y) such that Vf(x,y) =±(1, 1).

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.