If a, az, az is an orthogonal basis for R and b aa + azaz + azaz then O a. afai O b. afa Faz afa %3D

Q: Find a basis for R that includes the vectors (2, -1, 5) and (4, 5, -5) {(2, -1, 5), (4, 5, -5), )}

A: Idea is we try to find a vector which is not in the span of given two vectors now collection of…

Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

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Q: Write x as the sum of two vectors, one in Span fu1,u2,uz} and one in Span fu4}. Assume that fu, .u4}…

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Q: where B A = = H (a) Find At -6 rref (A). -1 -2 TATT -1 7 -4 -18 10 9 NAAN -1 1 -3 2 17 (e) Find a…

A: (.) Note: '' As per guidelines we will solve first three subparts. If you want any specific subpart…

Q: (b) The general fact that fcu++eUn]e== c\]j + .. + ca[vn]s allows for rewriting the equation above…

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

Q: 6- Check if each of the following is orthogonal or not: i- A = ii - A = iii - A =

A: We have to check the given matrix  is orthogonal or not

Q: If A is diagonalizable then A´is diagonalizable. Select one: O True False

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Q: Which of the following vectors form an orthogonal basis? 2 [0] T- 1] 3 го а) -1 4 b) -2 3 剛 2 -2' 3…

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Q: Show that the vectors a = (1,0,-1), az = (1,2,1), az = (0,-3,2) form a basis of R. Express each of…

A: It is given that

Q: 0. The vectors 2 0 , and 1 form a basis ofR. 3 3 a) True b) False

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Q: Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given…

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Q: 1 3 -2 4 Find the row space and null space of A = -1 2 . Write each as the span of a basis. -6 4 -8]…

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Q: 5. Given the bases B and C, and the given vector in one the bases, find the coordinate vector in the…

A: Please see the below pictures for detailed solution.

Q: 5. The conjugate of 2√7-√√3 is: a) √3-2√7 b)-2√7 + √3 d) 2√7 + √3 c) √7 + √3 6. In R³, the standard…

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Q: - 10 -8 2 4 -6-8 16 2 of A with the given orthogonal basis. 6 1 4 11 6-3 16 30 23 4 4 1 An…

A: We have to find the  factorization of the matrix

Q: Let S = {ax? + bx + a : a, b ɛ R}. Then a basis and the dimension of S are (a) basis: x2, x + 1;…

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Q: Let -2 4 -5 A 4 -3 Сл 5 -2 4 -5 A basis for the column space of A is { }. vector

A: A basis for the column space of matrix A is given by the set of columns corresponding to the pivot…

Q: vecterd (l,l.3) .c2.3.6] a (libis) form Do the budia fer R?

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Q: Let e1, e2, e3, e4, ē5, e6} be the standard basis in R°. Find the length of the vector * = 471+…

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Q: b) Give an example of a set of nonzero vectors in R3 that generates R3 but is not a basis for R3.…

A: The answer is given as

Q: 11 In the standard basis the coordinates of a vector are Xs -7 - (E) 2 In which of the bases given…

A: Given 6 bases for the vector space R3. Given vector Xs with respect to standard basis.

Q: Find all values of a e R such that {(1,2,5), (a, -2,5), (-3,6,5)} forms a linearly independent set…

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Q: a. Find a basis for the rowspace of A. b. find a basis for the columnspace of A.

A: Given Matrix A=12310abc12 We are also given a=0, b=1, c=7 Hence matrix A becomes A=1231001712

Q: Find a basis for the column space of 1 0 1 47 A = -3 -3 3 3 5 3 -1 5 Basis =

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Q: 4. * Determine if the set B is a basis of R. 4a) B= 4b) B=

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Q: 1. Let 3 -6 -4 7 -2 -3 A = 5 3 7 6- -1 A basis for the null space of A is { }. vector

A: Basis for null space of A

Q: За Let W be the collection of all vectors in R3 of the form a – 2b [5а + b! | а. Give a basis for W.…

A: Let W be the collection of all vectors in ℝ3 as of the form 3aa-2b5a+b. a) Give a basis for W. b)…

Q: Find an orthogonal basis for the column space of the following matrix 0 1 1 1 2 -M = 1 0 0 21

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Q: find matrix B line basis of the plane IR the mirror reflection I of R is of Spanned by F27 -1 So…

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Q: Determines whether or not the given set of vectors is a basis for the R² space. justify your answer…

A: A Given set of vector is −4,4,4,8. We have to determine whether or not the given set of vectors is a…

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.