The projection of y onto i is a scalar multiple of y.

Q: Let u = 21 - j, v= 6i + j, and w = i+ 4j. Find the specified scalar. u•v+u•w

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Q: Find the scalar product a•b when (i) a= x+2y -z and b=2x+3y +z (ii) a=x-3y +z and b=2x+y +z

A: We have to find the scalar product a·b when (i). a=x+2y-z and b=2x+3y+z(ii). a=x-3y+z and b=2x+y+z

Q: Let u = 3i - j, v= 3i + j, w =i+ 2j Find the specified scalar. u• (v + w) :

A: Solve the following

Q: Find the vector projection of onto v. u = 12i + 3jP + 4k U = i + j +k>

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Q: Let x, y, and z be vectors in Cn and let a and B be complex scalars. Show that a ( z, x) +B ( z,y )…

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Q: (a) Prove that if u is orthogonal to both v and w, then u is orthogonal to v + w. (b) Prove that if…

A: Given: (a) If u is orthogonal to both v and w. To prove:  u is orthogonal to v + w. (b) If u is…

Q: Let u = 5i -j, v = 3i +j, w=i+2j %3D Find the specified scalar. (4u) v (4u) • v = %3D

A: 4u=45i^-j^=20i^-4j^ Then, 4u.v=(20i^-4j^).(3i^+j^)=60-4=56

Q: Calculate the scalar triple product u · (v × w), where u =〈1, 1, 0〉, v =〈3, −2, 2〉, and w =〈4, −1,…

A: The vectors are, u=1,1,0v=3,-2,2w=4,-1,2 We need to find the scalar triple product u·v×w

Q: Let u be a vector in R² whose projection onto the x-axis is shown in the figure. Determine the…

A: Given:

Q: The scalar product 0v is 0.

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Q: Find the centroid of t

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Q: Let V=R^2 and let H be the subset of V of all points on the line 2x+3y=6. does H contain the zero…

A: Given  V=R2 and let H be the subset of V of all points on the line 2x+3y=6.

Q: Find the scalar and vector projections of b onto a. a = 3i - j + 4k, b = j+ (1/2)k 1 compab = V 26 1…

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

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Q: Let u = 2i - j, v = 3i + j, and w = i + 4j. Find the specified scalar 5(v . w)

A: Given vectors are: u=2i-jv=3i+j and, w=i+4j We have to find the value of 5v.w Here we have to use…

Q: Verify that the function f(z) = Z is continuous throughout the complex plane.

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Q: Find the scalar and vector projections of b onto a. a = b =

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Q: Given the two vectors: å = 2ỉ -j+k, b = i + 2k and d = 3ỉ + 5j in 3D. a) Determine the dot product…

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Q: Find the projection of u onto v.

A: Given,            u= < 2, 1, 3 > and  v= < 1, 0, -4 > and w = < 1, 1, 5 >

Q: Let u = 10i + 2j, v=i+j, and w = i-j. Find scalars a and b such that u = av + bw. a = b =

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Q: Find the scalar and vector projections of b onto a. a = (1,6), b = (-7, 1) compab = projb =

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Q: 1 Find the vector projection of u onto v. u= 3i- 5j ++ 2k v=7i+j- 2k

A: Please refer the attached image for complete solution.

Q: Let u be a vector in R2 whose projection onto the x-axis is shown in the figure. Determine the…

A: From the given figure, it is observed that the coordinates of the projection of U onto x-axis is 3,…

Q: Let u = 2i - j, v = 3i + j, and w = i + 4j.Find specified scalar 4(u . v).

A: it is given that, u = 2i - j, v = 3i + j, and w = i + 4j

Q: Find the scalar and vector projections of b onto a. a = 3i - j+ 6k, b = j+k = j+ k compab = projąb =

A: Here we find the scalar and vector projection of b→ onto a→where a→=3i∧-j∧+6k∧ , b→=j∧+12k∧

Q: Let u = 2i - j, v = 3i + j, and w = i + 4j. Find the specified scalar 4(u.v)

A: Given that u = 2i - j,   v = 3i + j  and  w = i + 4j. Obtain 4u·v as follows.

Q: Prove that if u is orthogonal to both v and w, then u is orthogonal to sv+tw for all scalars s and…

A: Given that u is orthogonal to both v and w.

Q: Let Q be an orthogonalmatrix such that QA makes sense. Show that (QA)+ = A+QT.

A: The (Moore-Penrose) pseudoinverse of a matrix generalizes the notion of an inverse,somewhat like the…

Q: If o is a scalar point function and c is a scalar then prove that grad (c o) = c (grad o). %3D

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Q: Let u = 7i- 3j, v= i-j, and w= i+j. Find scalars a and b such that u = av + bw. a = b=

A: We will find a and b

Q: Let u= 4i-j, v= 5i + j, w=i+2j Find the specified scalar. u• (v + w)

A: The given vectors are u=4i-j, v=5i+j, w=i+2j

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

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Q: Let L be the line in R that consists of all scalar multiples of the vector 2 Find the orthogonal…

A: Concept:

Q: Let u = 2i - j, v = 3i + j, and w = i + 4j.Find specified scalar (4u) . v.

A: The vector are given as, u=2i-j , v=3i+j and w=i+4j. To find: the value of 4u.v Solution: The value…

Q: Let u = 2i + j, v = i + j, and w = i - j. Find scalars a and b such that u = av +bw.

A: Given u = 2i + j, v = i + j, and w = i - j.Plug them in the equation u = av +bw.

Q: Determine a scalar r such that Ax = rx, where 1 A = and X=

A: Given, A=2112, x=11

Q: Find the scalar and vector projections of b onto a. a = 3i – j + 4k, b = j+ ÷k

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Q: Determine a scalar x so that the given vectors are orthogonal. A = xi +-j +xk 2. B =-3i +4j + xk

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Q: Let u = 8i + 2j, v=i+j, and w =i-j. Find scalars a and b such that u = av + bw. a = b =

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Q: Denote three scalars A = eTE-le, B = µTE-le and C = µTE-'µ. 1. Prove that AC – B² > 0.

A: We are given three scalers A,B,C in terms of weighted matrix inner-products, and we have to prove…

Q: Q4: Find the vector projection of u 6i + 3j + 2k onto v =i- 2j 2k and the scalar %3D component of…

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Q: snip1

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Q: Show that if k is a scalar and A is n × n, then det(kA) = kn det(A).

A: Show that if k is a scalar and A is n × n, then det(kA) = kn det(A). For any scalar k, we need to…

Q: Find all scalars c, if any exist, such that i+ cj + (c – 3)k is in the span of i+ 5j + 2k and - 5i +…

A: To Find: All scalars c, if any exist    such that i→ + c j→ + c-3 k→ is in the span of i→ + 5j→ +2…

Q: Calculate the scalar triple product u· (v x w), where u = (1, 1, 0), v = (2, –3, 5) and w = (4, –1,…

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Q: Let u = 4i- j, v= 2i + j, w = i+2j Find the specified scalar. u• (v + w) u• (v + w) = %3D

A: We have to do dot products of vector.

Q: Let x, y, and z be vectors in Cn and let α and β becomplex scalars. Show thatz, αx + βy} = α z, x} +…

A: Given: z,αx+βy=αz,x+βz,y

Q: b.) Determine the os culating plane of R.

A: