3 Find the coordinates of y 7 relative to the orthogonal basis Uj = U2 = U3 = -2 -4 10 2 2 4 252

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Q: Compute the orthogonal projection of v= 7 onto the line through 4 2 and the origin.

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Q: state a vector with all non-zero entries which is orthogonal to v⃗

A: Given v vector  Let w vector be orthogonal to v vector  Then w vector . v vector = 0

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A: The given two vectors are  v=-6i+10j-k  and w=2i+j-k

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Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

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Q: Find the coordinate vector of P relative to the basis S = {P1P2.P3} P1 = 1 +x+x*,P2 = x + x, p3 =…

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A: None option is correct. The details solution of the given question is given below in step 2.

Q: Select the option that gives the vector product of i+k and i + j Select one: 01 Oi+j-k Oi-j-k…

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Q: 2. In each question, explain the reason. Consider the following vectors in R³: (a) (b) v₁ = (1, 0,…

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Q: Find the projection of vector u⃗ = −i + 5j + 3k onto the vector v = −i + j − 3k?

A: Projection of vector u on vector v is given by  Projv(u) = u.vv2 v Here u = -i+5j+3kv = -i+j-3k…

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Q: Calculate the scalar products of the following vectors: 10 1 Q-B 5 W1 -4 9 (a) V₁ = (b) V2 = (c) V3…

A: Note: As per rule I need to solve only first three subparts.

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A: It is an important part of statistics. It is widely used.

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A: To find out solution of homogeneous set of linear equation of A's we have to find the solution of…

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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.