xample: Solving Axb, Ux = c, and Rx = d 1x1 + 2x2 + 3x3 + 5x4 Ax=b is 2x₁ + 4x2 + 8x3 + 12x4 = 3x₁ + 6x2 + 7x3 + 13x4 = 4- bi b2 b3 1. Reduce [A b] to [U c], to reach a triangular system Ux = c. 2. Find the condition on b₁, b₂, b3 to have a solution. 3. Describe the column space of 4: Which plane in R³? 4. Describe the nullspace of A: Which special solutions in R4? 5. Find a particular solution to Ax=(0;6;-6) and the complete x+x. 6. Reduce [Uc] to [R d]: Special solutions from R and. Xp from d.

Q: Use the left to right addition method as outlined in the module to add the numbers. For the middle…

A: Explanation of the answer is as follows

Q: To yield solution set of equations, system of equations used in form of O A+X = B+X OBX = A OAX = B…

A: We write the system of equations as AX=B And then we solve the system. So, A+X=B+X, BX=A, AB=X are…

Q: a) In a school of 36 students, 19 of them studies Music and 16 studies Art. Each student studies at…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: Q3./ Solve the following simultaneous ODE y₁ = -3y₁+ Y₂ −3 y₂ = Y₁ - 3 Y₂

A: To solve the  given problem, we use the standard defination of differential  equations

Q: Owen was constructing a uniquely shaped bird feeder for his Mom for Mother's Day. The bird feeder…

A: The volume of a hemisphere of radius r is calculated using the formula: V=23πr3. The volume of a…

Q: C D A B Consider the graph given above. Give an Euler path through the graph by listing the vertices…

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Q: (B.) L ( ³x ++ -cost} { +4- dt 3 dx dt Where: x(0) = x '(o)=6 and x" (0) = 2

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Q: P₁ (3, 65, -9) P₂ (5,12,8) Required solve 1) In the following points given Ps ( 8, 15, 23) P4…

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Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

A: Please see the attachment

Q: 7.) x = y² +₁₁ x = 0, y = -1 and y=2. The volume of the solid generated by revolving region about…

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Q: Let h(x) = f(g(x)). If ƒ(2) = −2,ƒ' (2) = -5, g(-6)= 2, and g'(-6) = 5, find h'(-6). Do not include…

A: It is known that: ddxf(gx)=f'(g(x))g'x.

Q: Q5. B. Solve the following first order differential equation using Linear method? ty' +2y=t²-t+1…

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Q: 2- Let the probability density function of the random variable X is - {²()* Then My(t) is (a)…

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Q: Find the area of the region bounded by x = y³ - 4y² + 3y and the x = y²-y. 77 (a) A= square units 12…

A: Given curves are x=y3-4y2+3yx=y2-y The curves intersect when…

Q: 5. The linear least squares approximation which best fits the curve y= |x | over the interval -1 ≤ x…

A: Sol

Q: Given that L{cos bt}(s) = S use the translation property to compute Leat cos bt}. s² + b²,

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Q: These values have an average of 8. What is the average distance of those values from that average of…

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Q: When using Runge-Kutta method of order 4 to solve the initial-value problem: ý = cos 2t + sin 3t, 0…

A: K1= 0.25

Q: c. A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Sol

Q: Suppose z = x + iy and f(z) = z - 1. Find w = u + iv such that f(w) = 1 + 3i (A) 3+2i (B) 3-2i (C)…

A: We have given that , fz = z - 1 , where , z = x + iy Here , w = u + iv Let , fw = 1 + 3i We need to…

Q: b. Let P (t) is the population of a certain animal species. Assume that P(t) satisfies the logistic…

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Q: Q3/ find the Fourier series for the following function. F (t) = ( 0<t<2 2<t<4

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Q: Evaluate ¹ (x²+x²2²)dzdx by using polar coordinates.

A: We have to evaluate the given integral using the polar coordinates. First we have to identify the…

Q: Determine the values of a, if any, for which all solutions of the differential equation y" − (2a −…

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Q: 2. Use ratio test to determine whether the following series is convergent or divergent: (2n)! Σ n.…

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Q: 2(a) Explain centroid of a triangle and rectangle with sketch.

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Q: дz in terms of r and t using chain rule if given that z=√√√4x² - y²₁ 1) Find and simplify dt x=r…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: The Nueva Ecija Feeds Inc. Produces specially blended feed supplements. It has an order of no more…

A:

Q: 3. For n x n matrix A. define R₁ = one of the Gerschgorin's disks {z: Iz-a₁j | ≤ R}. O True O False…

A: Statement: For n×n matrix  A. Define Ri=∑j=1,i≠jn|aij|, then, each eigenvalue of A is either in one…

Q: The upper triangular matrix U in the LU decomposition of matrix given below 25 54 10 0 U11 0 0 1 0…

A: Given: 2554081601222=100l2110l31l321u11u12u130u22u2300u33 To find u12,  u22,  u33.

Q: Find all x ER that solve this equation: 123 = x - (2x - (3x − 3) − 2) + 100+20+3

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Q: Q8. Find, if possible, the sum of each of the following series. Give exact answers. 3.2k α) ΚΕ Σκ 1…

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Q: Compute the definite integral T/4 0 5 sin² (3x) dx

A: Sol:- ∫0π45sin23xdxTake the constant out:  ∫a·fxdx=a·∫fxdx=5·∫0π4sin23xdx=5·∫0π4121-cos6xdxTake the…

Q: Plot the following planes and the normal vectors of each plane. 3x - 6y +9z = 9 x - 2y + 3z = -4 2x…

A: We will use inter relation between planes to find there relation . As solution of two graphs gives…

Q: 5. The sequence of partial sums of the equation Σ (a)3/2 (b) 3/4 3n-1 (c) 1/3 (d) -1/3

A: given expression ∑n=1∞13n-1

Q: 4. Evaluate //F FdS, where F(x, y, z) = (2x + 2xz, -4xy², y - z2) and R R surface of the solid…

A: The given problem is to evaluate the given surface integral over the given solid surface bounded by…

Q: Activity # 4: Inductive and Deductive Method A. Use inductive reasoning to guess the next three…

A: # As per the guidelines we are entitled to solve one question at a time (maximum three subparts)…

Q: Construct a graph with vertices F, G, H, I, J, K, L that has an Euler path, the degree of L is 1 and…

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Q: A population has the following characteristics. (a) A total of 75% of the population survives the…

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Q: Find the equilibrium point (q. p) for a product whose supply and demand equations are 35q-2p +250 =…

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Q: e. To solve the 2nd order ODE, x y" - (x + 1) y' - y = 0, by series method, the indicial roots are…

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Q: Simpson's 1/3 Rule can only be applied when the number of segments or strips used to approximate the…

A: Sol:-

Q: The error will disappear when using f(x)=x* to find the Lagrange interpolating polynomial p(x) if n…

A: Sol

Q: Q5): Determine the Fourier series of the function f(x) = 1 - x² in the interval [-1, 1].

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Q: The lower triangular matrix L in the LU decomposition of matrix given below is 25 5 1 0 111 112 113…

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Q: a tank holding initially 100 L of a salt Consider solution begins to flow into the tank at a…

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Q: ! d. Suppose that the cylindrical tank in the accompanying figure is filled to a depth of 4 feet at…

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Q: Solve the following system using Gauss Jordan method? x + 3y + z = 10 x-2y-z = -6 2x + y + 2z = 10

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Q: Item 2. Use the long cut procedure of Taylor series of expansion in determining the power series of:…

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Q: Q/find the Domain and the range. ofthe function f(x) = _5X х2 -3х+4

A: We have Fx=5xx2-3x+4 Now, we factor the denominator. We have x2-3x+4 The solution of ax2+bx+c=0 is…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.