OIISIUET quatioIS 8. 6. (a). 4 6. 6| + x2 |5|+ x3 3 X1 %3D 1 X4 – 2x6 0 + x2 |1|+ x3 (b). -X5 x1 1 1 -X5 X6 1.1. Write down each equation in the matrix form Ax = b. 1.2. Find the general solution of each matrix equation, expressed in vector form.

Q: 20.Consider a 2 × 2 system x′ = Ax. If we assume that r1 ≠ r2, the general solution is…

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Q: For the tableau, X2 32 KHS 38 2 49 -5 -4 perform one pivot operation and enter the resulting matrix…

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Q: 2- For any constant matrix A, if A² = 0 then a- e4' =I +At b- e4 =I - A12 c- e At-A²1 ² The correct…

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Q: 2. Let 2 25 and B=| 32-1 23-2 A = 23 7 a) If possible, invert the matnix A b) then solve the matnx.…

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Q: [2.26] Construct a general solution of the system Ax = b where A is an m x n matrix with rank m.…

A: The answer is given below:

Q: 3. (a) Solve the matrix equation for X: -1 0 1 1 2 1 1 -3 1 -1 3 1 -1

A: If Ais a m×n matrix and B is a n×p, then AB is m×p Hence here X is 2×3 Let X = abcdef Thus…

Q: [3 -4 |1 2 10 3 -1 6x -9 4 2 15. Solve for x and y in the matrix equation below: -8 4 3 -1 -3 3r 0

A: As per our guidelines we are supposed to answer only one  question. Kindly repost other question to…

Q: solve X′ = AX by providing two linearly independent solutions of the form v(t). In each case…

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Q: 2. Find the values of x such that the rank of matrix 3x – 8 3 3 3 За — 8 3 - 3 3 3x – 8 is less than…

A: See the attachment

Q: 6. Use the Gaussian Elimination (a) to write the following augmented matrix in the reduced row…

A: We Know that,  A matrix is said to be in reduced row echelon form when it is in row echelon form and…

Q: '8 5 For the matrix A = (2 5 4 \4 4 9. cofactor C23? A. - 7 В. 12 С. — 12 D. 7

A: 1) The given matrix is A=850254449.

Q: Q2 • Represent the initial value problem Q Q1(0) = 6; Q½ = 3 = 4 with a matrix equation 12 3 •…

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Q: 2r + y + 3z = 1 2r + 6y + 8z= 3 6x + 8y + 18:=5 Solving the system of linear equations by Gaussian…

A: We have to find Solution of given System of linear equations by Guass Elimination Method for…

Q: 3. Local pollution levels are determined by p(x;y) : R² →→ R', where x is the number of…

A: The Hessian matrix (H) is defined by,                                           H = fxxfxyfyxfyy…

Q: 2. Find x, y and z x- 3y + 5z = -9 2x - y-3z = 19 3x +y+ 4z -13 %3D (a) Use inverse matrix method…

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Q: Give general solutions for x,(t) and X2(t) dx, = x1 + 3x2 +1 dt dx2 = 3x1 + x2 +1 dt

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Q: Find the general solution to the system x' = Ax where A is the given matrix. -1 4 A= -1 3 2 +C. e -…

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Q: 4. Our definition of an invertible matrix requires that A be a square n x n matrix. Let's examine…

A: A=-1-1-2-130        B=-2211-2-1

Q: 11.) Solve using matrices and Gaussian elimination: x+y+z= 9 -x-3y + 2z = 10 2x + z = 9

A: Please see the below picture for detailed solution.

Q: Reduce the quadratic ferm 34*+5y+32²- Caronical form matrix of t rans 2 2 + 2z x to the and 8pecity…

A: Our main interest lies in finding a suitable orthogonal transformation X=PX' which will reduce the…

Q: Given formula z= In /x*² + y**³ . From the experiment, we obtained x=5 and y = 2. Find the maximum…

A: For the given values of a, b, c and d, we get, z=lnx4+y11and x=5 and y=2error of value x is…

Q: 1. Solve for X in the given matrix equation (A -X) =B where 1 1 2 and B = -1 ol A 3 2 21

A: A and B are determinant matrices

Q: 26. If r3 +9x + 5 is divided by x, then remainder is 27. Find the value of x in the equation 2 log3…

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Q: (b) Table Q4(b) is generated from the function ƒ(x)= e* - 4x² + B , where B is the last two digits…

A: Given: fx=ex-4x2+B To find: f'1.5

Q: -9 -9 -42 -36 Let A = and let B = 3. -8 33 15 Solve the matrix equation for X : 3X = 3A –B. ЗА -В.…

A: Divide both sides by 3

Q: x + 2y – 2z + 3w = 0 2x + 4y – 3z + 7w = 0 -x – 2y + z – 4w = 0 3x + 6y- 5z + 10w = 0 %3D In #1(b)…

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Q: Find the root of f (x) = x2 -2x - 2,correct 3 dp, using Newton-Raphson method.

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: 11.) Solve using matrices and Gaussian elimination: x + y + z = -3 -x + 3y + 2z = -8 2x + z = -3

A: Given: x+y+z=-3 -x+3y+2z=-8 2x+z=-3

Q: 2D grae Q1 (а) f(x) = Vc² – x² where c- The last digit of your matrix number For example, a student…

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Q: Find the elementary matrix E₁ such that E₁A = B where A = 8 9 1 7 -17 −1 18 1 10 and B = 18 7 8 1…

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Q: Solve A x A T matrix: A = -2  1  -1 3   -3   2

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Q: Q1: find values (if any) of the unknows x & y which satisfy the following matrix equations? [3 -4 -5…

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Q: You are given the 3 x 3 linear system in augmented matrix form 5 0 -1 2 0 1 0 2 0 0 2 4 Starting…

A: We have. 50-1201020024 Thus, we have 3 equations: 5x+0y-z=20x+y+0z=20x+0y+2z=4 From the above…

Q: ind the general solution to the system x ' = Ax where A is the given matrix. -4 -2 A= -3 -3 2 D O…

A: For this problem, first we will find out the eigenvalues of the matrix A and corresponding…

Q: [1 2 1.5 In the augmented matrix for what value(s) of the parameter h does the system have a NO…

A: Here, the matrix is, A=123h

Q: [1 2 1 0 0 Is the matrix E = 0 0 1 0 0 0 0 0 1 0] in reduced row echelon form?

A: yes this is the matrix in reduced row echelon form

Q: 1. Find the co-efficient matrix for the given linear equations 4x1 - 3x3 + X4 = 1 5x1 + x2 - 8x4 =3…

A: We use the definition of the coefficient matrix to find the answer of the given question.

Q: x-2 1. A= 3x-6 4x-11 Given that the matrix A is singular, find the possible values of x.

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Q: 3. (a) Solve the matrix equation for X: -1 0 1 2 0. 1 1 3 1 1 3 1-1

A: Explanation: To solve the matrix equation. X-101   110   31-1=120  -31-1 The resultant matrix is…

Q: of linear equations correspondingto the coefficient matrix A below. 6 -2 01 -6 -5 0 1 20

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Q: Solve the nonhomogeneous system of differential equations 8 -2 2 8 d -2 8 2 x - e 2t 16 dt 2 8 24…

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Q: l6 WHe the augmented matrix as asycten of equa ions. Fd o -3 100 O 200 E3 | -5 350 メナーリ Z= xt yt_ Z=

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Q: 4. The reduced row echelon form of a matrix A E M75(F) has 3 zero rows. What is nullity(A)? Justify…

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Q: 1. Find the inverse of the given 3x3 matrix. By Gaussian elimination. 2 2 31 3 1 1 %3D [10 3 4] show…

A: The solution is given as

Q: -2 9 For the matrix B = 1 if |B| = 0, what is the value of y? 1 Y 93m3

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Q: 2. Solve and express the solution to the following reduced row echelon form matrix equation in…

A: The solution is given as

Q: A is a (3 x 4) matrix with the only special solutions= to the equation Ax = 0. nd the rank and the…

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Q: 4. Consider the matrix equation Ax = b where, A = a b 1 1 where a, b > 0. (a) When is A strictly…

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Q: 8 5 0 For the matrix A = ( 2 5 4 cofactor C23? 4 4 9.

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Q: Archie gave Oscar a matrix -3 0 4 A = 1 -3 0 where c and d are mystery real numbers. d Oscar applied…

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Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.