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: 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: DO NUMBER 5 (Linear Alegbra & Diff. equations)

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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, 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: -B 2. Given: A = 2 -4 0 2 1 -1 2 1 2 3 1 -2 1 4 4 a. Transform A into RREF then give a basis of its…

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Q: Find an orthonomal basis of U = span 2 00 -2

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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: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: Let T: P2 → P2 by T(ax? + bx + c) = (12a + 5b – 5c)x² + (-20a – 8b + 10c)x + (10a + 5b – 3c); a the…

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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: Consider the basis B3 = (x² - 1, x, 1) of P2 (R). Find [2x² + 3x − 5] B (2,3,-5) (2,3,-3) (3,2,-5)…

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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: 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 = {2 + 3x², 10 + 4x + 15x², 26 + 8x +36x²} is a basis for P3. Find the coordinates of p(x)…

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Q: {} W = span D. -C If A is an orthonormal basis for VĀ w, then A= a= ,b= B= C= %3D are all positive…

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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

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Q: What is [p]B, the coordinates of p = 4+ 7x with respect to the standard basis B = {1, x} of P1? Ex:…

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Q: The set B = {2 + 2x², 4 − 3x + 4x², 19 − 9x + 18x²} is a basis for P₂. Find the coordinates of p(x)…

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Q: Show that B = {1,1 – x,2 – 4x + x²,6 – 18x + 9x² – x³} is a basis for P3(R). Hint: Recall that…

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Q: The vectors B [x] B = = {[H∙A} form a basis. Find the B-coordinates of x = 4 4

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Q: Consider the following "standard" basis of R³ over R: --000 = Let q be the real quadratic form (from…

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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.