Suppose A E R4×3 has the following QR factorization A QR V2 -V2 [1 0 1 0 0 0 0 -1 1 1 1 -1 R = 1 Find an orthonormal basis B for imgA.

Q: The set B= {2+z, 6+3z + 3z,- (23+9z + 12z*)} is a basis for P Find the coordinates of p(z) = - (73 +…

A: Coordinates

Q: Let W = } t s,t e R -S - 31 5) Show that -6 is in W+. 3 6) Find a basis for W+.

A: given W=s+3tt-s-t  , s t ∈R

Q: Let 9. A = 3 9 4 6. -3 2 -2 Find an orthonormal basis of the kernel of A.

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Q: Let 1 1 -4 A = -3 9 -6 -2 8 -7 Find an orthonormal basis of the column space of A. 4 -18/5 -6 36/5

A: Consider the matrix A=[11-4-39-6-28-7]We find the basis for the…

Q: Explain why S is not a basis for P2. S = {1 - x, 1 - x², -1 – 4x + 5x2} O sis linearly dependent. O…

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Q: The set B = {4+x², 20 - 3x+5x2, 45-6x + 11x2} is a basis for P2. Find the coordinates of p(x) = 6x -…

A: 30-1Explanation:

Q: Explain why S is not a basis for P2. S = {1, 4x, -9 + x², 7x} S is linearly dependent. O s does not…

A: Given S={1,4x,-9+x2,7x}. We explain why S is not a basis for P2.

Q: Find a basis for the ideal √(x³ - 214 + 2x² - x, x5-14-21³ + 2x² + x − 1). ស

A: We have to find a basis for the ideal x5-2x4+2x2-x,x5-x4-2x3+2x2+x-1

Q: Given an orthonormal basis of R³ : {V1, V2, V3} = = 2 [] 7 is expressed as a linear combination u =…

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Q: 1) Consider the basis V = (e₁, e₁+ e2, e2+ e3, e3+ e4) of F4. Find the dual basis V

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Q: Answer all the questions: (2 1 1 1. The characteristic polynomial of the matrix 0 1 0) is A1 1 2. a)…

A: Here the given matrix is                                        211010112 We have to find the…

Q: 1 Which of the following is a basis of R4that includes the vectors and 1 ? 1 -1 1 1 1 1 1 1 -1 1 1 1…

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Q: Define T:R-→R² by T(x) = Ax. Find a basis B for R² with the property that [T]B is diagonal. - 3 - 3…

A: Given:T:ℝ2→ℝ2 is defined by Tx=AxWhere A=-3-3-1-5To find basis B for ℝ2 such that TB is diagonal.…

Q: Which one of the following is an orthonormal basis of R³? 1 {]--]} {B}. √3 √2 3 {]···]} √2 2 √6 0 /6…

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Q: The set B = {3 + 2x², 6 − 2x + 4x², 4x − 13 – 10x²} is a basis for P₂. Find the coordinates of p(x)…

A: The objective of the question is to find the coordinates of the polynomial p(x) = 18x - 54 - 40x^2…

Q: JApply the Gram-Schmidt process to 2 -3 a1 a2 a3 3 1 to obtain an orthonormal basis for Span{a1, a2,…

A: a1=1-100, a2=20-20, a3=3-331 Consider v1=a1=1-100 v2=a2-a2, v1v1, v1v1=20-20-221-100=11-20

Q: If b1, b2 form an orthonormal basis for C and x is any vector in C, then O x4- x bị x b2 0 O x+ x bị…

A: We will find out the required value.

Q: Explain why S is not a basis for P2. S = {1 – x, 1 – x², –1 – 4x + 5x²} S is linearly dependent. S…

A: Given a set S={1-x, 1-x2, -1-4x+5x2}  To Explain why S is not a basis for P2.

Q: Which one of the following is an orthonormal basis of R³? {Q.0·0} 1 1 امام امامت امام 0 3 0 L √2 0…

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Q: Let v = 3 2. 2. What is the smallest positive

A: Given vectors are: v1=1122 ; v2=1232 ; v3=2134 ; u=321x We have to find the smallest positive…

Q: The set B = {− (1+3x²), − (2+2x+6x²), − (6+4x+21x²)} is a basis for P2. Find the coordinates of p(x)…

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Q: 1 -1 -4 3 -4 0 A basis is {v1, v2} where Let A 5 V1 || - Find a basis for Nul(A)+. V2 C

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Q: asis: The set B = {2-3x², 8+x-12x², 33x² - (21+ 2x)} is a basis for P₂. Find the coordinates of p(x)…

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Q: Given the basis B = the basisi B | {Q.B]} Find the change of coordinates matrix from the standard…

A: We find required matrix.

Q: 0555 if A = 0 0 0 0 then the basis fqf 0 205 N(A") is 1 .a Hạmmad Selawe .b كواے 1 .c 0.

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Q: Define a basis v1, v2 of R² by vị obtained by applying the Gram-Schmidt Procedure to v1, v2? 2 by…

A: Consider the provided question, A Basis of a vector space. Let V be a subspace of Rn for some n. A…

Q: The set B = {3 − 3x², 15+ 4x − 15x², 48x² - (47+ 12x)} - - is a basis for P2. p(x) = 12x² [p(x)] B…

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Q: 5

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Q: 7

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Q: Let V1 = [0, 0, 5, 0], V, = [3, 4, 0, 0] and V3 = [4, 0, – 2, – 4] Use the Gram-Schmidt procedure to…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Let TilPe P. Tlax²+ bx+c) = 20x+ b. Then the basis of NIT) is O True O False

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.