Show that if PER"×" is an orthogonal projector, then P+ = P.

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: One of the following vectors lies in span{ 2+x + x?, 3+x- 2x2} (A) 4+ x – 7r² (B) 4+ x – 4x? (C) 4 +…

A: Solve the following

Q: How do you know that for all a, b, c, d: ax + bx will be orthogonal to cx? + d ?

A:

Q: Suppose v, w, z are vectors in R". Show that if r and y are linear combinatio: v, w, and z, then r+…

A: Linear combination of the vectors

Q: (a) Prove that u + vand u - v are orthogonal in IR" if and only if ||u|| = ||v||. (b) Draw a diagram…

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

Q: Consider j1,ỹ2, ỹ,ER° and that ỹ,+y;+ÿ;=0. For Î=span{ÿ, ,ÿ and Y=span{ÿ2, ÿ}, show that Ý=Ỹ.

A: Given y1→, y2→, y3→∈ℝ5 such that y1→+y2→+y3→=0. Let Y^=spany1→,y2→ and Y~=spany2→,y3→. To show…

Q: If W(-10, 4), X(-3, -1), and Y(-5, 11) dassify AWXY by its sides. Show all work to justify your…

A: Given,           If W-10, 4, X-3, -1, and Y-5, 11 of ∆WXY.

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

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Q: Let S in Mzx2; a + 2d=0 and b-2c 0 with the standard %3D operations in M2x2 Which of the following…

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Q: Find the family of orthogonal trageclarnes fo he for

A: Given that            y3 = k x5 Here we have to find the family of orthogonal trajectories to the…

Q: { (0,3), (0,1) is linearly independent in R? ylgn O Ins

A: The given vectors are  (0, 3) and (0, 1) To find whether they are linearly dependent or not

Q: Find midpoint M of P,P2, which joins P1(5, -7, 2) and P2(2, 5, 6), as shown in Figure 10.46 of…

A: Formula used : Mid-point formula Mx1+x22,y1+y22,z1+z22 Here (x1,y1,z1) and (x2,y2,z2) are the end…

Q: show that the scalar t that minimizes ||y– tx||

A: In this question, we need to find the t that minimizes ||y-tx||.

Q: Suppose that a linear transförmation / satisfies T(u,) = T(u,) = -1 -2 Find T(4u, - 3u,). T(4u, -…

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Q: Find the value of k for which the vectors 4 and 4 k are orthogonal. k =

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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: - Show that the vectors X, - () 5e3t and X2 = ) 2et 7et form a linearly independent set.

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Q: Use the indicated entry as the pivot and perform the pivoting. $3 z 0 0 60 o ol 80 1 0 300 0 10 X1…

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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: Verify that it is orthogonal to both a and b. (a × b) · a = (a × b) · b = %3D

A: Given

Q: a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal, (b) Draw a diagram…

A: a) Suppose u,v are orthogonal. Now…

Q: Show that if, in using the Laplace development, you accidentally multiply the elements of one row by…

A: A 3×3 matrix a11a12a13a21a22a23a31a32a33.

Q: tnd the kes reetor projection of anto r if

A: Given : u→=5i→+2j→ and v→=6i→-3j→

Q: Show that if v and w lie in the yz-plane, then v × w is a multipleof i.

A: Both vectors v and w lie in the y-z plane, which means they must have zero magnitude component along…

Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: If v = 2i + 4j and w = -2i + 6j, find the vector projection of v onto w.

A: Given vectors are: v = 2i + 4j w = -2i + 6j The formula for the vector projection of v onto w is…

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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Q: "Span(u1,..., in) = Span(71,..., Tn, w) if and only if J1,..., Un, w are linearly depen- dent."

A:

Q: Mark the following statement true or false:

A: Mark the following statement true or false, In ℝ3, if non zero vectors u and v are not parallel,…

Q: Use the Wronskian to determine if the function vectors 7,= x? + e* and 72= e²x are linearly…

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Q: Suppose a and b are vectors such that axb=(1,

A: Given, a→ and b→ are vectors such that a→× b→=(1, 0, 2).

Q: Suppose Q : R? → R is a quadratic form such that Q(x) = 1 for all vectors X E R? Cuch that

A: Given: It is given that the quadratic function Q:R2→R such that Q(x)=1 for all vectors x∈R2 such…

Q: Consider the vectors x"(t) = (10) and x"() - 8t

A: Given, The two vectors  and

Q: Suppose vi, v2, ..., m is linearly independent in V and w ɛ V. Show that v1, vz, ..., Um, W is…

A: v1, v2,......., vm is linearly independent in V and w∈V

Q: 4. let f(x, y) = x² – xy + y² – y. find the direction u and Duf at Po(1,–1) for which Duf is the…

A: Given:- f(x, y) = x2 -xy+y2 -y To find:- Direction u and Du f at point p0 (1, -1) for which Du f is…

Q: The Canonical form of a hyperbolic PDE is F (ξ, η , u, ug , un ) %3D False True

A: To check the given statement is true or false. Given that the canonical form of a hyperbolic PDE is…

Q: et §, ŋ, o be real numbers and consider ctors (1,5,§³); (1,ŋ,n³); (1,0,0²). Determine e conditions…

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Q: The vector E = = -a, – 4as + 3a, expressed in RCS and in terms of ø is Е 3 (-сosф + 4sinф)ax +…

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Q: at x and y are orthogonal

A: Given: x and y in ℝn, x+y=x-y To show:  x and y are orthogonal in ℝn if and only if x + y = x − y

Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w?

A: x is orthogonal to v and w. Then their dot product is zero. That is, ⇒x·v=0  &  x·w=0

Q: Show that the dyfferential equatian IS exact x(スt5in t) do + cast -2tu) abe +x² dt-

A: We will show that the given differential equation is exact.

Q: What are the perpendicular generators on (P) to 4 %3D of the surface

A: Given equation s are, x216-y24=z....1x3=y2=z-4...2 Equation of generators of the hyperboloid (1) are…

Q: b) Show that the following wo matricegane orthogonal tker A =-V3 -2VTO 3/T15 15 E/NTS

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

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Q: If v1, ..., V5 are in R' and v3 = 0, then {v, V2, V3, V4, V5} is linearly dependent. %3D

A: Definition used: v1, v2, ..., vk is linearly dependent if there exist numbers α1, α2, ..., αk, not…

Q: Find the norm of the image of U(7, 8) by an reflection about y-axis

A: To Determine :-  The norm of the image of U 7 , 8 by an reflection about y- axis.

Q: One of the following vectors lies in span{ 2+ x + x2, 3+x- 2x2} (A) 2+ 2x + 7x? (B) 2 + 2x + 5x? (C)…

A: The linear span of the given vectors is of the form a(2+x+x2)+b(3+x-2x2)

Q: (f) Find the length of the projection of i onto ū.

A: Given