(b) Find the orthogonal decomposition of v with respect to W. projw(v): %3D perpw(v)

Q: Calculate F. dĩ, where C is the square of (1,1, 1), (–1, 1, 1), (–1, –1,1) and (1, –1,1), with…

A:

Q: Consider the vectors i = (2, – V3, 1) and ū = (-1, v3, 4). Find the orthogonal decomposition of u…

A:

Q: Calculate F . dr, where C is the square of (1,1, 1), (–1,1, 1), (-1,–1,1) and (1,–1,1), with…

A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: Given that xo= -1 and x1=1. Then the basis of the first Lagrange polynomial Lo(x) and L,(x) are…

A: Given that        x0 = -1 and x1= 1 On the basis of the first Lagrange polynomial we have to find…

Q: 3. Compute the inner product g (v,w) of v = + x. 2 əx and w = x.-+ 2y. Əx ay' Where the line element…

A:

Q: Given ABCD and its image EFGH in the plane, which type of transformation has taken place?

A: There are many different rules that are used to transform a figure into another figure. We an…

Q: 2) Let f(x,y,z) =x²y³z* Use the Lagrange multiplier method to find the maxi- mum value of f on the…

A:

Q: Consider the following. u = -7i - 4j - 2k, v = 4j + 4k (a) Find the projection of u onto v. -12 2k X…

A: Given :u=-7i-4j-2kv=4j+4k

Q: Find the vector projection of b = 6î + 3ĵ + 2k onto å = î – 2ĵ – 2k.

A:

Q: A) compute x the component of x that is parallel to L and x the component of x that is orthogonal to…

A:

Q: b) Find A6 for A = by using the advantage of the diagonal representation by similarity…

A:

Q: The scalar product 0v is 0.

A:

Q: Parametrize the directed line segment which joins the point −2 + 3i to the point 5 − 7i, that is,…

A: The parametric equation on a line passing through the points x1,y1 and x2,y2 is given as follows:…

Q: The orthogonal projection of v = 10i on b = −3i + j is _____ .

A: To find the orthogonal projection of v = 10i on b = −3i + j .

Q: Use the given transformation to evaluate the integral. (12x + 12y) dA, where R is the parallelogram…

A:

Q: 3- The scalar component of the vector F in the direction of K is (K.F А- .K, В- K C-

A:

Q: Determine the residual and Jacc - bian needed to solve the equation d²u 2u° = 0, - dx? 1 and u(1) 0,…

A:

Q: nd the orthogonal trajectories of the family of confocal central conics given as: = 1 a² + à b² + à

A:

Q: find all the scalars k such that || kv || = 3, Where v = (-1, 2, 0, 3)

A:

Q: Find the cross product ⃗a × b and then specifically verify that it is orthogonal to both ⃗a and b:…

A: Given data:     The first vector is: a=<a1, a2, a3>=<6, 0,-2> The second vector is:…

Q: Find all values of the scalar k for which th e two vectors are orthogonal.

A:

Q: Find the orthogonal projection of y onto u. y = -3/5] - 4/5 /5 4/5 b) c) d) 2.

A: The formula to find the orthogonal projection of y onto u is: projuy=u→.y→u→2.u→ Here,…

Q: Find the coordinate vector of p(x) in P., relative to the basis S= {p,.P.-P;}, where p(x) =…

A:

Q: b) Use the transformation u = 2x – y, v = x + 3y to find p (2x-y)3 dA, x+3y where R is the…

A: .

Q: 21. Apply the conjugate-gradient method to the problem Ax = b, where 1 A = 1 1 %3D and b = 1 Verify…

A:

Q: Consider an inner product on two P₂ vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(2)g(2): 1) (−4 +…

A: The inner product on two P2 vectors as f,g=f-1g-1+f0g0+f2g2

Q: Q8) The planes 3x+6z=1 and .2x+2y-z=3 are orthogonal F O

A:

Q: The orthogonal projection of the vector v =3i-j+k on the vector b 2i-j+k is

A:

Q: 10) Find the cross product a x b and verify that it is orthogonal to both a and b. a =  j + 7k,…

A: Let's find.

Q: (a) Determine all the elements in the -1 + V-3 stabiliser of z = under the 2 action of SL,(Z) on the…

A:

Q: Use the given transformation to evaluate the integral. + v), y = v - 3u) (16x + 16y) dA, where R is…

A:

Q: use the inner product = p(x)q(x)dx. to find the projection of p(x) q(x) = 5x + 2. = S'; x3 onto

A:

Q: Find the Jacobian of the transformation. x = 4v + 4w?, y = 9w + 9u?, z = 5u + 5v2 Ә(х, у, 2) d(u, v,…

A: Given transformation: x=4v+4w2y=9w+9u2z=5u+5v2 We have to find the jacobian  ∂(x, y, z)∂(u, v, w).

Q: Let A ∈ M nxn(F). Show that A is diagonalizable if and only if At isdiagonalizable

A:

Q: d) Find the orthogonal projection of v = 1 into U+. (1)

A:

Q: 2: Find the component of u = 2i+j - 3k that orthogonal to v = 3i – j, then verify your result.

A: Solution:

Q: Use the given transformation to evaluate the integral. (12x + 12y) dA, where R is the parallelogram…

A:

Q: Use the given transformation to evaluate the integral. u + v), y = v (16x + 16y) dA, where R is the…

A: Given  ∬R16x+16ydAWhereR is the parallelogram with vertices -3,9, 3,-9, 4,-8, -2,10and x=14u+v ,…

Q: (b) Perform the Gram-Schmidt orthogonalization process for u = x +1, u2 = x? + 3, u3 Va using the…

A: b. Given that               u1=x+1, u2=x2+3, u3=x Using Gram-Schmidt orthogonalization process for…

Q: Let T : R² → R³ be the linear map given by [2r1 + 7x2] 2i + 22 Write does the matrix A associated…

A: The given linear map is T:ℝ2→ℝ3Tx1,x2=2x1+7x2, x1-x2, x1+x2 To find the matrix A associated with T…

Q: Current Attempt in Progress Let a = ci +jandb = 9i + 45j. Find c so that a and bare orthogonal. c =…

A: Given :a=ci+j and b=9i+45jTo find : The value of c so that a and b are orthogonal.

Q: Find the determinant of the linear transformation. T(f(t)) = f(3t – 2) from P2 to P,

A:

Q: The orthogonal projection of v = 10i on b = –3i + j is <

A:

Q: Find the image of | z – 3i | = 3 under the mapping W =-.

A:

Q: B.4 Find the orthogonal projection of the vector (1,2..n) on the orthogonal complement M- of M in E…

A: The complete solutions are given below

Q: Let S be the parallelogram then determine the area of parallelogram by the vectors [h and b2 h/2 [1…

A: The parallelogram is determined by the vectors  b1→=hh2=10251                              (since…

Q: Find the orthogonal projection of v=2 onto W.

A:

Q: Use the given transformation to evaluate the integral. (9x + 9y) dA, where R is the parallelogram…

A: This question is based on the concept of change of variables in double integral whose formula is…

Q: (b) Perform the Gram-Schmidt orthogonalization process for u = x +1, u2 = x² + 3, u3 = Va using the…

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.