Show that the system x' =Ax has constant solutions otherthan x(t)= 0 if and only if there exists a (constant) vectorx ≠ 0 with Ax = 0. (It is shown in linear algebra that sucha vector x exists exactly when det(A) = 0.)

Q: assume that Pr[A′]=0.55, Pr[B]=0.35 , and Pr[A′∩B]=0.2. (1) Pr[A∩B]=Pr[A∩B]=   (2)…

A: Solution : Given information; P(A')=0.55 P(A)=1-P(A')=0.45P(B)=0.35 and P(A'∩B)=0.2

Q: Identify the maximum value and the corresponding unite vector of the quadratic form Q = x1 3a²³ —…

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Q: If T is defined by T(x) = Ax, find a vector x whose image under T is b, and determine whether x is…

A:

Q: Consider the following ordered basis for P₂ (R): B {x²+2x+1, x + 1,1} [] 3 2 (a) What quadratic…

A:

Q: If Q : R" → R is

A: (a) Given, if Q : ℝn→ ℝ is a quadratic form

Q: Prove that x(t) = xoe At xoe At is unique solution

A:

Q: Is {x² – 2.x, x²+x, x²} linearly independent dependent? Prove your answer. or

A: Answer

Q: Suppose v, w e R" and {v, w} is linearly independent. Prove that {v – w, 2v+w} is linearly…

A:

Q: ppose S = &v₁₁ ore that T = nearly independ

A: Answer given below.

Q: (d) X₁ = {(1,0), (0, 1), (1,1)} CR² (e) X5 = {(1,0,0), (0, 1,0), (1, 1, 1)} CR³ (f) X6 = {(1,0,0),…

A:

Q: Let A 2 -5 6 ✓ 5 -2 6 Select true or false for each statement. b 2 [1].. True 1. The vector c is in…

A:

Q: Q3. Determine the kernel and range of each of the following linear operators on R³: (a) L(x) = (X3,…

A:

Q: 4. Prove that, for any vectors A, B and C, a necessary and sufficient condition that A x (B x C) =…

A: Given: Three vectors A,B, and C. To Prove: necessary and sufficient condition for A×B×C=A×B×C, is…

Q: Computations: [7x -3y 9. Compute a basis of x, y E R x + y

A: We will find out the required basis.

Q: (7) Given the following pieces information, describe the set of solutions x such that Ax = b: (a) b…

A: We shall solve first question only as you have asked more than one unrelated questions • for others…

Q: 2 3 [+0 4 2 b = -2 Select true or false for each statement. Let A = and c = [12] 1. The vector c is…

A: The objective of the question is to determine whether the given vectors b and c are in the kernel…

Q: If Q : R" → R is a quadratic form, then Q(x) attains its maximum and minimum values on ||x|| = 1 at…

A: Given statement is that if Q:ℝn→ℝ is a quadratic form, thenQ(x) attains its maximum and minimum…

Q: Prove that the two solution functions in Attached Theorem 4 are linearly independent.

A:

Q: Show that for binary vectors, wt(u + v) ≥ wt(u) - wt(v) and equalityoccurs if and only if for all i…

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Q: 4. Let p(x) = a + a₁x + a₂x² and q(x) = bo + b₁x + b₂x² be vectors in P₂ with: (p, q) = aobo + a1b₁…

A:

Q: 8

A: According to the given information it is required to determine whether the given set is linearly…

Q: = Let p(x) = x³ x² + 2x + 3, q(x) = 3x³ + x² − x − 1, r(x) = x³ + 2x + 2, and s(x) = 7x³ + ax² +5.…

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Q: How many solutions does Ax = [1]   have?

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Q: w+y+2z w+2x-y -3 2w+x+3y-2z ] = [X²] 6 x-2y -2 0

A:

Q: Let us say that you are sitting at a coffee shop and you want to impress your significant other by…

A: As per bartleby guidelines for more than three subparts in a question only first three should be…

Q: Show that u = (a, b) and v = (e, d) in K? are linearly dependent if and only if ad – be = 0.

A: Solved below

Q: 4. In the vector space P3(R), let S = {p1(x), p2(x), p3(x)}, where P1 (x) = 63x° + 19x² – 37x – 41,…

A: (a) we see, p2(x) = -3p1(x), so S is not linearly independent. [Ans] (b) As S is not linearly…

Q: (a) Prove that for every positive integer n, one can find n + 1 linearly independent vectors in…

A: (a) To prove that for every positive integer , one can find linearly independent vectors in…

Q: T: ([₂]) = 3x1 +4x2 x1 - 2x2 4x1

A:

Q: If the set {(1, 2, 1), (0, 1, 1), (1,–1, A)} is linearly independent, then (A) A# -2 (B) A # 2 (C) A…

A: The objective is to find the correct option.

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.