Find bases of the kernel and image of the orthogonal projection onto the ry-plane in R*. basis for the kernel is basis for the image is

Q: Let 7 = -27+ 7+2k and w = 3 7 +23- k. (a) Compute the vector projection of w onto , proj- w. (b)…

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Q: Consider the following maps of polynomials S:P →P and T:P→P defined by S(g(x)) = 4 g (5) – g'(-2)and…

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

A: The given vectors are u=3,3 and v=2,0

Q: Find the bilinear transformation which maps the points (-1,0,1) into points (0,i,3i)

A: the bilinear transformation which maps the points (-1,0,1) into points (0,i,3i)

Q: Orthogonalize the basis {(1, 1, 1, 1),(1, 1, −1, −1),(0, −1, 2, 1)} by the Gram-Schimidt process.…

A: Let x1 = 1111 ; x2 = 11-1-1 ;  x3 = 0-121      Using Gram schmidt process , we get orthogonal…

Q: Show linear dependence in part (ii) to show that ({1,0,1}) is a basis.

A: From part ii)We have to show that the set  is a basis of .We know thatA basis B of a vector space V…

Q: Find a basis of R3 that contains the vectors (1,0,1) and (1,-1,1)

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Q: Find the Bilinear Transformation that maps the points (0, 1, ) in z-plane onto the points (-1,-2,-i)…

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Q: linear operator T: P,P2 4. Cet the be defined by T(aotq, Xfayxtagx?)=3ast (az-93)x² a) Find a basis…

A: The given linear operator is                                               T : P3→P2 which is…

Q: Determine whether the set of vectors {(2,-1,3),(4,1,2),(8,-1,8)} form a basis for R3.

A: Consider the vectors : 2,-1,3, 4,1,2, 8,-1,8 To form a basis these vectors, the vectors must be…

Q: Use matrix multiplication to find the orthogonal projection of (-8, 5, 7) on the xy-plane. Let T…

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Q: Please discuss your understanding of what a basis is for a vector space

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Q: Prove that a(-3,2) and b (2,-3) form basis vectors in xy plane

A: a set is said to be basis if set is linearly independent and it spans the space.

Q: Find an orthonormal basis of the plane x₁ +4x2x3 = 0.

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Q: 3. Let L: R* → R³ be defined by U1 U1 1 1 1 U2 U2 1 2 1 Let S and T be the natural L U3 U3 1 -2 1 U4…

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Q: Create a basis of R¹ containing vectors (1,-1, 3, 2) and (2, 1, 3, 4) by adding basis vectors of the…

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Q: What are the spline basis functions for a cubic spline basis with 3 knots at values x1, x2, and x3?

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Q: Find an orthonormal basis of the plane x₁ + x₂ + x3 = 0

A: The given problem is to find the orthonormal basis of the given plane. Given plane is x1+x2+x3=0

Q: Consider C^4 as a vector space over C. Find a basis of C^4 containing the vectors (i, 0, 1, i) and…

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Q: Let v1=( 0 1 -1 2)^T v2=(1 0 -2 1)^T Let V=Span{v1,v2} Find a basis for the orthogonal complement of…

A: Orthogonal complement : Let V be a vector space in ℝn. The orthogonal complement is the subspace…

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: 3) Find a basis of F3 containing the vectors (1, 2, -3), (2, 6, -3)

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Q: Suppose V is a subspace of R" and suppose {v1, v2, v3} is a basis of V. Decide if the following sets…

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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.