Find || A||1, || A||0. Find an r + 0 so that || Ax|| = ||A||||| for each norm. 2 4 A = 3 -7 -1 -8 1 -2

Q: . Rewrite the equality of ideals (r+ y/2) = (3 – 4/2) in Z[/2] in terms of elements.

A: We know that, A subring  B of a ring R is called a ideal of R if for every r∈R and for every b∈B,…

Q: Prove that for all a € R, 0 < r² + 2 VI

A: Prove the following

Q: Define sets A and B as follows  A = { n E Z | n = 6r+4 for some integer r and B = { m E Z| m = 18s…

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Q: Let v= -2 then the first norm of v equal 7 -3 Select one: O True O False

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Q: To prove the Cauchy-Schwarz Inequality u v < ||u|| ||v||, for any real number t, 0 < (tu + v) · (tu…

A: Let u and v be two vectors and a, b are real numbers. Use the following formulae, to prove the…

Q: For every real m x n matriz mx m) and a diagonal m x n matriz

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Q: Let M = {-x² + 2,x + 1, 2x}. %3D Which of the following statements is true about M?

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Q: . Let A = {x € U|x is a multiple of 2} {x € U|x is a perfect square} B = ind each set. a.) AUB b.)…

A: Topic:- set theory

Q: The Fibonacci numbers 1, 1, 2, 3, 5, 8, 13.. are defined by the recursion formula xn+1 = Xn + xn-1,…

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Q: Prove by direct proof: “V n E Z if 2 ł (3n + 5), then 2 | n."

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Q: II. Prove the following using Direct Proof. . If x and y are perfect squares, then xy is also a…

A: In mathematics and logic, a Direct Proof is a way of showing the truth or falsehood of a given…

Q: Let M = {x + 1, x2-2,3x). %3D Which of the following statements is true about M? O None of the…

A:

Q: Let A = AB= 1 -1 2 0 5 1 -2 0 −1 14 -57 3 [-2 27 -32 0 -5 2 -1 1 0 -7 1 X -2 and B = 5 2 Find x such…

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Q: Find all (real) values of k for which A is diagonalizable

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Q: Find the maximum possible order for some element of Z, x Z1, x Z18 O 50 O 150 O 90 O 80 None of them

A: Given problem is :

Q: A __________ in the variable x is a finite sum of terms of the form axn where a is a real number and…

A: A polynomial P(x) is defined as

Q: If T: R"„8* is a Linear transfor matiom and m (x)= (2² +2)Cx+ 3. Find all the ratinal canomical ferm…

A: Companion matrix:  Let f(x)=xn+an-1xn-1+………+a0 be a polynomial then the matrix form is given by…

Q: Which of the following statements are true? I: If F, and F, are 5-dimensional flats in R', then the…

A: Given that F1 and F2 are 5- dimensional flats in R7.

Q: ind ATA and AAT. 1 3 -3 -2 -4 4 A = 5 0 0 1 8 3 (a) ATA (b) AAT Vhich of these products is…

A: Here we have to find the product of ATA and AAT .

Q: (k) If x, y, and z are integers and xylz, then x|z and ylz.

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Q: (c) Let z1 = 2+ 2i and let 22 =1+i. Prove that the triangle inequality |21 + z2| < |21| + |22|…

A: Left hand side is equal to, z1+z2=2+2i+1+i=3+3i=32+32=32 Right hand side is equal to,…

Q: Determine the least-norm solution to the following: X1 з01-11 x2 -1 20 -3] x3 –12 X4 274 77 4 12 11…

A: Step:- 1 Given system is 301-1-120-3x1x2x3x4=-124 of the form Ax=b Here, A=301-1-120-3, x=x1x2x3x4…

Q: 1. Let x, y, and z be real numbers. Prove the following: [a] -(-x)=x [b] (-x)y = -(xy) and (-xX- y)=…

A: "By Bartleby rules, only first three sub-parts of question 1 have been answered"

Q: Determine a and b such thatp(x) = x2 +ax+ bsatisfies p(l) = 0 and p' (1) = 4.

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Q: 2. Find the (infinity norm) condition number of 2.01 1 (b) A = 3 6.

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Q: Find all (real) values of k for which A is diagonalizable

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Q: Prove or disprove: If T is 1-1, then T2 is 1-1. Prove or disprove: If T² is 1-1, then T is 1-1.

A: Answer

Q: Find the value(s) of k such that A is singular.

A: A matrix is singular if its determinant value is zero. So we find the determinant value of the given…

Q: -1 Let v=-2 then the first norm of v equal 7 -3 Select one: O True False

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Q: 2. Z [x] is a principal ideal domain. a) True b) False O a) True O b) False

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Q: 9- Z is Principal Ideal Domain. a) True b) False O a) True O b) False

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Q: The value of k such that P2(1) = 2.8 , 2 k 4 1 Is

A: Lagrange's interpolating polynomial is:…

Q: . Which of the following is the counterexample of: For all real numbers x, x≥1.  a. 12 b. 22 c. −12…

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Q: |u|> c is true for all real numbers if c _ 0.

A: |u|&gt;c is true for all real numbers if c ____ 0.

Q: 1 Let v=-2 then the first norm of v equal 7 -3 Select one: O True O False

A: The 1-norm of a matrix is the maximum of the absolute column sums.

Q: Given de - and d, - Then do and d, are not G- conjugate if Gis Non of these -0.25 105. 0.25 -0.5 -0…

A: We want to find the matrix G for which given vector are not G conjugate

Q: - For a positive integer n, le Pn(r) = (x + 1)(r+2) (x + n). Show that the set of polynomials Pn (x)…

A: Here, we want to show that the set {pn(x)x+1,pn(x)x+1,...pn(x)x+1} is linearly independent. A set…

Q: Let a, b and c be positive numbers such that a ^ 2 + b ^ 2 = c ^ 2 Show that a + b> c.

A: Let a, b and c be positive numbers such that a ^ 2 + b ^ 2 = c ^ 2To Show:-  a + b&gt; c.

Q: Let 1 3 A = -2 -1 and В - 2 -2. a. Find AT and show that (A")' = A. b. Show that (A+B)" = AT + B".…

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Q: Let a; b; c 2 N such that a + b = c. Prove that gcd(a; b) = gcd(a; c) = gcd(b; c).

A: The given problem is to prove the following condition for given equation a+b=c, where a,b,c belongs…

Q: Find the value of k such that A is singular. 0 3 2 -1 0 L 3 3 k k =

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Q: let a>0. prove that if x is a number such that |x-a| a/2

A: Given a&gt;0 and x is a number such that x-a&lt;a2 We will use the property If y&lt;b , then…

Q: (b) Let A = a + 1 and B = b+ 12. Using proof by induction, show that A+B divides An+1 + Bên+1, What…

A: here i used basic condition of divisibility and i used the notation a|b for a divides b .

Q: Find the domain of gof, iff(x) =x² and g(x) = Vx-6. %3D O a.l-, - võJU(võ. x) O b. (-30, -6]U[6, ¤)…

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Q: 1. Suppose a and b are real numbers. Prove that if 0< a < b then 1/b < 1/a

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Q: The norm of the set {e-8inx},n e N, "<xs in the Hermitian sense is А. В. С. D. 8. E. None マド」。

A: Use the formula of the norm to determine its value. The function and the limits are given.…

Q: Determine all natural numbers a, y and z such that z < y < z, and xyz + zy + cz + yz+x + y+ z+1=…

A: Given, xyz+xy+xz+yz+x+y+z+1=2020 (xyz+xy)+(xz+x)+(yz+y)+(z+1)=2020 xy(z+1)+x(z+1)+y(z+1)+(z+1)=2020…

Q: Q3) Prove or disprove (if the question is true prove it, otherwise give an ехample).

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Q: Let A={x:xER and x is a solution of x²+2=0},then A is a null set ylgn ihi

A: We have to check whether the statement, "Let A=x:x∈R and x is a solution of x2+2=0, then A is a null…

Q: b] { c d [a 1. Prove that I= a,b,c,d are even integers} is an ideal of M2(Z). %3D

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.