Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (1, −4)

Q: Find uxv, vx, and vx V. U= i +j, v=j+K U × V

A: using cross product of vectors...

Q: Express dw/ðr and ðw/ðs in terms of r and s if w = z² + y°, x =r – s, y=r +8.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Write v as a linear combination of u and w, if possible, where u = (2, 3) and w = (2, -1). (Enter…

A:

Q: Find fx and fy, and evaluate at the given point.

A: The given function is: fx, y=xyx-y and the point is 2, -2. To find the fx and fy, first…

Q: Find V · (V × F), if F(x, y, z) = 7e**i+9xe³j – eu=k. V·(V × F) =

A: Given thatF→=7exzi+9xeyj-eyzkto find ∇.∇×F

Q: Find and ds using the chain rule: W = x? + y?, x = s+t, y = s – t

A:

Q: Find V. (V x F), if F(x, y, z) = 7e**i+ 8xej – 3elk.

A:

Q: Find the following statement is true? ' W[y1,y2] = 0 implies y1 and y2 are linearly dependent'

A:

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = i + 2j − k, v = i + j + 2k

A: Given vectors are (a)

Q: U W V

A:

Q: Find the linearization at the point indicated:   V (h) = 4h(2 − h)(4 − 2h), a = 1

A: Given: Vh=4h2-h4-2h ,a=1

Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

A:

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = i − j, v = j + k

A: Given: Two vectors are . In part (a) Find the vector product of two vector u and v. therefore the…

Q: Determine the linear dependence of fi(t) = t + 2, f2(t) 2t2 + 3t, and %3D II f3(t) = -t2 +3.

A: Given functions are f1t=t+2f2t=2t2+3tf3t=-t2+3 To determine whether f1,f2,f3 are linearly…

Q: (a) Find x, y el such that x+y || x || .. = 1 = || y || = || ** ||**y. ∞o 2

A:

Q: Find u x v, v × u, and v × v. u = i - j, v=j - k V (a) u x v (b) v x u (c) v x v

A:

Q: Example: If w = f(x,y), find d²w dr² x = et, and y = 2t - 1

A: Here, w=f(x,y), x=et, y=2t-1

Q: Solve for w where u (1, 1, –1, 0) and v = (2, 3, 0, –1). %D 5w u - 4v %3D W = Submit Answer

A: Solution:-

Q: Find u x v, v x u, and v X V. u=i-j, v=j-k

A:

Q: Find the cross product a × b. a = (t, t2, t3),      b = (1, 6t, 8t^2)

A:

Q: Find (a) v x w ,(b) w x v ,(c) w xw ,and (d) . v x v .

A:

Q: Find (a) v x w ,(b) w x v ,(c) w xw ,and (d) . v x v .

A: Solution:Given    v=-i+3j+2k              w=3i-2j-kFind:(a)v×w(b)w×v(c)w×w

Q: Solve for w where u = (1, 1, 0, -1) and v (0, 3, -1, 2). w + 4v = -3u %3D

A:

Q: Find ||u||, ||v||, and ||u + v||. u = -2, V = 5, (a) ||u|| (b) ||v|| (c) ||u + v||

A:

Q: let r (t) = The y component of r' (5)

A:

Q: find the Jacobian ?(x, y)?(u, v) for the indicated change of variables. x = u + 1, y = 9v

A:

Q: Determine values of x and y so that v · w = 0 and v · u =

A: There are vector representation given as, v=x1y , w=x-20  and u=0-9y. To find the value of  x  and y…

Q: Which of the following are first order linear aiterential equations? F. = y – 3y

A:

Q: Suppose u=, v=x +y and w w(u.v): a) Express W and W, in terms of W. . X and y b) Calculate xW, +yw,…

A:

Q: If f(u) : f'(u) = V13 + w'dw then

A: Let,

Q: Calculate r' (t), T(t), and T(2) where r(1) = (3, r*). r' (t) = ( 6t ). ... ... ... 4t^3 ... T(t) =…

A:

Q: Express w as a linear combination of u and v. 1 - 5 u = V: w = - 9 w = u+

A:

Q: Calculate r'(t) and T(t), where r(t) = (2t – 5, 4 – 4t, 1 + 4t). %3D r'(t) = { %3D T(t) = {

A:

Q: Find 2 (v x u), given u x v = (-, 5, 8). %3D

A: u×v=-83, 5, 8

Q: Write v as a linear combination of u and w, if possible, where u = (1, 1) and w = (1, -3). (Enter…

A:

Q: Find the point P such that v = PQ has the components (-1.75, –8.75, 2.5). Q = (1.25, 1.25, 5.5) P =

A:

Q: Find u · (v ✕ w).

A: Here we have to find the given vector operation

Q: Find a and b such that v = au + bw, where where u = (1, 2) and w = (1, -1). v = (0, 24) V = a = b =

A:

Q: Find x, y, z, and w. x 2 (2x - 1) (2x - 2) y 7 3y (w + 1) (2y + + 3) y = = M x N W

A: Given:x22x-1y73y=2x-2z33w+12y+3

Q: Write v as a linear combination of u and w, if possible, where u = (2, 1) and w = (2, -2). (Enter…

A: u=2, 1 and  w=2, -2To express v=4, -1 as a linear combination of u and w

Q: Which transformation should be use to make the equation Ty 3, y(1) : = 2 linear? %3D O a. y3 = v O…

A: We will find out the required solution.

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = i − j − k, v = 2i + 2j + 2k

A:

Q: x+y Show that: B(x+1, y) = B(x, y)

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

Q: Let V = {A, B, C} and T= {0, 1}. Find a) VXT b) T²,T³3,T4

A: Given V = {A,B,C} and T = {0,1} we have to find a) V × T b) T2 , T3, T4

Q: Use Cramer's rule to solve the set of linear equations x-2y- 3z =-1 3x + y-z =9 - 4x + 2y +z = 2

A: Here we have to use Cramer's rule to solve the set of linear equations.…

Q: If f(z) = z² - (z)² + zz, calculate the following: a) u(x, y) and v (x, y) b) u(-10,-5) and…

A:

Q: Find the value of x, y, a and b. 4. (x – j2y) – (y – jx) = 2 + j

A: Given, (x-j2y)-(y-jx)=2+j

Q: Write v as a linear combination of u and w, if possible, where u = (2, 2) and w = (2, -1). (Enter…

A:

Q: find the Jacobian ?(x, y)?(u, v) for the indicated change of variables.   x = u2 + v2, y = u2 − v2

A: We know that, the Jacobian of the transformation given by x = x(u, v) and y = y(u, v) is…

Q: Find r'(t), r"(t), and r'(t) r(t) = (t2 + 9t)i – 3t2j %3D -

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.