Use the summation convention and free subscripts to indicate the following linear system y1 = A11X1 +a12X2 Yz = a21x1 + az2X2

Q: Represent the given system by matric representation. 2x+4y =5 -x +3y =-2

A: Given a system of equation.  2x+4y =5- x +3y =-2 We have to represent the given system by matric…

Q: (a) Determine if the following system is consistent: X2 – 4x3 = 8 2x1 – 3x2 + 2x3 = 1 5x1 – 8x2 +…

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Q: Use the QR factorization to solve the system Ax %3D

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Q: The Cramer's Rule can be applied to find the solution of the system

A: Cramer's rule is applied to a system of n equations with n unknowns, represented by the system Ax=b,…

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: Write the following linear system 21 - 5x2 = 4 2x1 + 3r2 = -5 3x1 - 2x2 = 7

A: Given: x1-5x2=42x1+3x2=-53x1-2x2=7

Q: Use Cramer's rule to determine how many solutions the following system of equations has. -4x +2y +…

A: Use Cramer's Rule

Q: Solve the following linear system by Cramer's Rule: -2X - Y- 3Z= -3 2X - Y+ Z= -13 2X – 3Z = -11

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Q: Use Grammar's rule to solve the system -6x + 4y + 3z = 30 -2x + z = 6 3x – 2y – z = 8

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Q: Determine if the following system is consistent: X1 – 3x2 + x3 = 1 2x1 X2 – 2x3 = 2 xị+ 2x2 – 3x3 =…

A: Given; x1-3x2+x3=1 2x1-x2-2x3=2 x1+2x2-3x3=-1.

Q: 2. Use Cramer's Rule to solve the linear system. 16х, — 12х, — 12хз — 16х, = 16 -12x1 + 25x2 +x3 –…

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Q: Suppose that m>n in the homogeneous system                        a11x1+a12x2+…+a1nxn=0…

A: Here we have a system of homogenous equation with m equations and n variables  Now here m>n which…

Q: Write a note on a linear system Ax = b.

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Q: Consider the system below. Let a = 0. x1 = -x1x3 + ax1 x2 = -x2xỉ + ax2 A) Examine the stability of…

A: To Determine :-  The stability of the origin with the linearization method. x1˙ = - x1 x22 + a x1x2˙…

Q: Consider solving the linear system 2x1 + x2 – x3 + 2x4 4.x1 + 5x2 – 3x3 + 6x4 -2x1+ 5x2 – 2x3 + 6x4…

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Q: how to answer number 2?

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Q: X1 – 2x2 + x3 + x4 = 4 x1 + 2x2 + x3 + x4 = 1 2x1 +2х3 + 2х, 3D 5

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Q: Consider the linear system 3x1 --6x2 +3x3 +9x4 %3D 3. 2x1 -3x2 +3x3 +4x4 %3D -3x1 +7x2 -2x3 -10x4 -1…

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Q: Find 1) w(x,,x2,x3)for the system x, = tx,-2x2+3x3 1 x2= 5x,-3x2+X3 X 3 = - X2+ X3

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Q: Determine whether the system is consistent: a) x1−x2+3x3=−11     −4x1+4x2−12x3=44…

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Q: Solve the system of congruences x=7mod11, x=3mod7, and x=2mod5

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Q: Let A be the following system: x + 2y = 4 x - y = -2 2x + 2y = 1

A: As per the instruction, we will be solving the first one. For (a), We need to verify that the…

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: Find the nullspace of the system {4x1 – 2x2 (2x1 X1 + 2x2 – x3 – 4x4 + x5 + 2x6 = 0 + 3x5 – x6 = 0.…

A: We have to find a basis for the null space, we form an augmented matrix by appending a column of…

Q: Use LU-decomposition method to find the solution of the linear system: +2x, +3x3 = 6, 2.x, + 7x, +…

A: Given AX = B where                A = 12327114-6X = x1x2x3B = 6131 Let A = LU, where          L =…

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

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Q: Find a basis for the solution space of the following linear system + 3x2 + 4x3 + 5x4 201 + 6x2 + 9x3…

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Q: Decide which one of the following systems of polynomials is a linearly inde- pendent system: (i) x2…

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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: The linear system Ax=b is consistent whenever the columns of [A | b] are linearly dependent. True

A: Introduction: If and only if b is a linear combination of A's column vectors, a linear system Ax = b…

Q: Use Cramer's rule to compute the solution of the system. 4x1 + 2x2 = 8 3x, + 7x2 = 17

A: We will find the solution using Cramer's rule as following.

Q: A linear system is said to be overdetermined if there are more unknowns than equations Select one: O…

A: We know that system of linear equation is called overdetermined if number of equations is more than…

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: Solve the following linear system by Gaussian elimination. X1- X₂- 1 X3 Fill X1 + 3x₂ + 4x3-4 -X1 -…

A: The solution is,  x1=4x2=0x3=0

Q: (c) Show that the following linear system is a strictly diagonally dominant: 4x1 - X2 - X1 + 4x2 -…

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Q: Use naïve Gauss-elimination to decompose the following system. 7x+2x2 - 3x3 = -12 2r+Sx2 - 3x3 = -20…

A: Rewriting the problem in matrix form: Converting the coefficient matrix into an upper triangular…

Q: Solve the linear system using Cramer's Rule 3x + 6y + 5w - 3z = 32/5 28 5x - 3w + 2z = 15 - 62 5y +…

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Q: Use the summation convention and free subscripts to indicate the following linear system y1 = a11X1…

A: We will use the notion of summation and varying subscripts to write the system of equations into…

Q: Find x1, X2, and x3 of a given linear system using Crouts Method. X1 + 4x2 + X3 = 5 X1 + 2x2 + X3 =…

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Q: Consider the system Uz + 4uy = -2vy 2uy + 4vy = -Vx

A: Given: system of equation;  ux +4 uy=-2vy 2uy+4vy=-vx

Q: Determine which of the points (-3, –4, -6), (– 3,4, 5) satisfy the linear system 2x1 8x2 2x3 -48…

A: In this question, the concept of matrix multiplication is applied. Matrix Multiplication Matrix…

Q: Solve the following linear system by Gaussian elimination. X1 = X2 11 x3 = and X1 + 4x2 + 2x3 = 12…

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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: There is a linear system that has exactly 2 distinct solutions.  true or false

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Q: Show that the following linear system is a strictly diagonally dominant: 7x1 – x 2 = 9 -X1 +7x2 – X3…

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Q: Use naive-Gauss-elimination to decompose the following system. - 2x + 3y + z = 9 x + 2y + 3z = 6 3x…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.