1. 1 3 Let ui = 3 U2 -3 4 x = 1 3 Calculate the orthogonal projection of x onto H span{u1, u2}.

Q: 6. (a) Let u, v, w be three linearly independent vectors in Euclidean Space R^7. Determine a value…

A: we have to find the value of for the linearly dependent and linearly independent

Q: Compute the orthogonal projection of onto . Use the square root symbol 'V' where needed to give an…

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Q: 3) (i) Compute the vector projection of u onto v, proj u, where V u=(3, 3) & v= (2,0). (ii) What is…

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Q: Let a be a fixed unit length vector (A is in R^3). Define a linear transformation T: R^3 -> R^3 by…

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Q: Question 1 What is the scalar projection of the vector A=1 10 +-9 +2; onto the vector 6 +8 9 +02 if…

A: To find  The scalar projection of the vector A on to the B both are acting on the same line Q

Q: The projection of the point (2, -3, 1) on the yz- plane is Select one: O (0, -3,1) ○ (2,0,1) O (2,…

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Q: 月…- 2 Letting vi = 1 and vi = use Graham-Schmidt to find 0. orthonormal vectors (q1, q2}, and show…

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Q: Consider the point (3,4,5) What is the projection of the point on the xy-plane?

A: The given point is (3,4,5).

Q: (13) Let 2 * - ( 1 ) --- ()) + - (1) = = = 0 Show that Span (V1, V2, 3) = = ܕܐܐ ܕ Span(1, 2) and…

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Q: Find an algebraic description of the range of A by row reducing A^T and using the relation between…

A: We know that rank(A) = rank(AT). We need to find an algebraic description of the range of A by row…

Q: -2 12. Calculate an orthogonal projection of u onto v if u = 2 ,v = 2 3

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Q: let W be an inner product space and let w1 and w2 be vectors in W. suppose ll w1 ll =5^1/2 and ll w2…

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Q: 15 3. 1 and v2= - 9 description of Span (v, v,} for the vectors v, %3D 1: 3 ect answer below. 1.V}…

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Q: Let W1=span{(1,1,0),(-1,1,0)} and W2=span{(1,0,2),(-1,0,4)} Proove W1+W2=R^3

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Q: tind the equation of a polynomial Shose graph, passes through the points t-1,7), (0,2)(2;4)

A: As per guidelines I had solved the first question. Thank you.

Q: -}]-=[}]»=[}- [] 3 Find Let vị = and p = 3 a hyperplane [f: d] (in this case, a line) that strictly…

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Q: Let V be a finit dimensions vector space of at least dim =1, Let T: V-> V be a linear transformation…

A: Solution

Q: 2. Let y and u = Write y as a sum of two orthogonal vectors, one in Span{u} and a vector orthogonal…

A: y and u are given to us and we need to write y as a sum of two orthogonal vectors such that one is…

Q: Find ProjS(u) where S is the space spanned by v1= (1/3)(2,1,2) and v2= (1/3)(-2,2,1). Find the…

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Q: Let V be a finit dimensions vector space of at least dim =1, Let T: V-> V be a linear transformation…

A: Given that V be a finite dimensional vector space with dimension ≥1 and T: V→V be a linear…

Q: What is the vector projection of X = (7, 0, – 3) on ỹ = (-1,3,3)? Answer:

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Q: - [23²] 42-[ ] 4 - [3 ¹ A₂ = A3 = Let A₁ = A₂ + and B = n span(A₁, A2, A3)? No then express Bl as a…

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Q: e vector x²y?

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Q: 1. Let u and v (a) Draw u and v in R. (b) Use the parallelogram law to add 2u - v to your picture.…

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Q: Let $K$ is a horizontal shear, next draw a vector $\vec{x}=\left[\begin{array}{l}x_1 \\…

A: Let be the transfomation representing vertical shear of the vector  .Then we have The above can be…

Q: 1) (From Hardcover Book, Marsden/Tromba, Vector Calculus, 6th ed., Section 1.1., # 37 or from your…

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Q: 6) Let V,, V2, V3, V4 be four vector spaces with dimV, = 8, dimV2 = 5, dimV3 = 7, dimV4 = 6 Let T1:…

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Q: 7. (a) What is the projection matrix that projects all vectors in R³ onto the plane x+ y + z = 0?…

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Q: Find the particular number of orthogonal transectories of x2+cy2=1 passing through the point (2,1)

A: Given equation is x2+cy2=1........1. We have to find the particular number of orthogonal…

Q: B Gruien Vectors i = (2,1₁-4), ✓ = (-340,2) w (11213). Find onthogonal projection of u + v along…

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Q: 6. Project the vector b = (1, 4, 2) onto the plane S that contains the vectors a₁ = (1, 2, 1) and a2…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: