Prove that a linear system Ax = b is consistent if and only if the rank of (A | b) equals the rank of A.

Q: Solve the linear system Ax = b by using Cramer’s rule,givenCarefully explain all steps in your…

A: Given: A=342122301b=1−14

Q: Find the value of for which the system X-y = -2 is inconsistent. a X+ay = a

A: The solution for the above question is as shown below.

Q: Give attention to a nonhomogeneous linear system of the form?

A: The non-homogeneous linear systems of the form are-

Q: consider an arbitrary linear system with input x[n] and output y[n]. show that x[n]= 0 for all n…

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Q: By using Cramer's Rule , solve the system of linear oauation given by PX = C where if 3 C. and C =

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Q: 2) Is there a choice of rational numbers a, b, c, d for which the linear system has no

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 8. , determine conditions on the constants b, (b1, b2 etc), if any, in order to guarantee that the…

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Q: The linear system Ax=b is inconsistent if Rank(A) does not equal Rank(A |b) Select one: True False

A: We need to tell whether the given statements are true or false.

Q: Consider the following augmented matrx of a linear system of equations Axb. For which values) of h…

A: I have Provided this answer in step-2.

Q: Use Gaussian elimination to obtain an equivalent system whose coefficient matri echelon form. X1 +…

A: We are asked to obtain reduced matrix using  guass elimination method

Q: Find A, and b such that Ax = b corresponds to the given linear system. 7x1 – 4x2 – 3x3 = -6 - 5x1+…

A: 7x1-4x2-3x3=-65x1+4x2-8x3=2Ax=b7-4-354-82×3 x1x2x33×1 =-622×1

Q: Determine conditions on the b,'s, if any, in order to guarantee that the linear system is…

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Q: 1. Verify whether the vector X is a solution of the given system where 2. X' = X; X=

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Q: 1. Verify whether the vector X is a solution of the given system where X; X =| 3 X' =

A: Given:

Q: The linear system Ax=0 is always consistent Select one: O True O False

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Q: Use the Cramer's rule to solve the linear system: x + y = 1 1 x - y = 3

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Q: Find a basis for the set of solutions of the following linear system: x1 + x2 + x3 − 2x4 = 0 x2 −…

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Q: Verify that the following linear system does not have an innite number of solutions for all…

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Q: Determine whether the nonhomogeneous system Ax = b is consistent. If it is, write the solution in…

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Q: • Investigate the stability of the following systems (Consider the quadratic form as Lya punov…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Find all real number 1 such that the homogenous system such that (AI – A)X = 0 has a nontrivial…

A: A=-2000-23045 Consider, λI-AX=0 ⇒λ+2000λ+2-30-4λ-5x1x2x3=0

Q: Determine a basis for the solution space of this system

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Q: Show that the 3D system x' = Ax is conjugate to the system x' = -x where a < 0 and A is given by (a…

A: To prove that the 3D system x'=Ax is conjugate to the system x'=-x where A is given by  A=α100α100α,…

Q: Use the Gauss–Jordan method to determine whether each of the following linear systems has no…

A: AX=B110101101211348find the pivot in the 1st column in the 1st…

Q: Verify that the following linear system does not have an infinite number of solutions for all…

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Q: Let   X1+2(X2)+5(x3)=3 , 2(x1)+4(x2)+(a2-0)=b  , then the values of a,b such that the system is…

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Q: Find a basis for the solution space of the given homogeneous linear system- X – 2x, +3x, 2x, - 3x,…

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Q: Use the Cramer's rule to solve the linear system: [x + y = 1 1 x - y = 3

A: We will solve the given linear system of equation using Cramer's rule in the following step.

Q: Find the value of for which the system X+y 2 is inconsistent. X+ay = a

A: It is inconsistent problem.

Q: Determine conditions on the b;'s, if any, in order to guarantee that the linear system is…

A: First we will convert the given system of equation into Matrix form AX=B and then find the row…

Q: Let   X1+2(X2)+5(x3)=3 , 2(x1)+4(x2)+(a2-6)x3=b  , then the values of a,b such that the system is…

A: solution:-step-igiven,x1+w x2+5 x3=32x1+4x2+a2-6x3=bnow in this,a1=1…

Q: a system is constructed from two functions as , proof that such system is linear using a…

A: In the given question, the concept of  Superposition Theory is applied. Superposition Theory…

Q: Solve the following linear system of equations using Cramer's Rule

A: We have to solve the following linear system of equations using Cramer's Rule.

Q: 6. Use the Gaussian Elimanation to write the determine conditions on the c's, if any, in order to…

A: Given: A system x1-x2+3x3+2x4=c1-2x1+x2+5x3+x4=c23x1-2x2-2x3+x4=-c3-4x1+3x2-x3-3x4=-c4 To find:…

Q: What conditions must be satisfied by b1, b2, b3, b4, and b; for the overdetermined linear system X1…

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Q: Any inconsistent linear system can be solved using the Cramer's rule Select one: O True False

A: We tell true or false Any inconsistent linear system can be solved using the Cramer's rule

Q: Let A = - 1 Determine whether the Jacobi method applying for solving the linear system

A: The given matrix is 1-111

Q: Show that the 3D system x' = Ax is conjugate to the system x' = -x where a < 0 and A is given by 1 A…

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Q: Consider the nonhomogeneous system 2х, — 6х, + 3х, —-4 -X + x; + x, = 5 2.x; +6x, – 5.x, = 8

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Q: 4. Use Cramer's Rule to find x for the linear system given by x+ 2y – z = -1 3x – y + z = -6 2x - 2z…

A: The given linear system is                                          x+2y-z=-13x-y+z=-62x     -2z=-6…

Q: Use Gauss-Jordan elmination to find all solutions to the linear system: X1 + 3x2 + 2x3 + 4x4 X3 + X4…

A: NOTE: Refresh your page if you can't see any equations. . system Ax=b is

Q: The least-squares error of a system of equations Ax b is always unique. True False

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Q: X2 -1 1 -2 4. 3 X3 -3 2 2 X4 x5

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Q: Let Show that: If the homogenous system AX = 0 has only the trivial solution, then ad – bc # 0.

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Q: Find A, and b such that Ax = b corresponds to the given linear system. 5x1 + 3x2 + 6x3 = 7 2x1 + 8x2…

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Q: Evaluate the following linear system using Cramer's Rule: a. x-3y +3z=-4 2x+3y-z=15 4x-3y-z=19

A: The given system of linear equations…

Q: Is every homogeneous linear system always consistent? Explain.

A: To, Explain if every homogeneous linear system is always consistent.

Q: Solve the linear system Ax = b by using Cramer's rule, given 3 4 2 1 2 2 A = and b = 3 0 1 Carefully…

A: Solve the linear system Ax = b by using Cramer's rule, given               A = 342122301 and  b =…

Q: 2. Determine whether the linear system Ax = b is well- or ill-conditioned . You can use either the…

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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.