Find the inverse of the matrix and the identity matrix A= 4   2  - 3       1  -1   2       5    3   0

Q: 3y"' + 2y" = 0. y(0)=-1,y'(0)=0,y"(0)=1 Solve this

A: First of all write the characteristic equation of given differential equation and solve it for root'...

Q: This is one question but I couldn't fit the whole question in one photo so I attached two photos, th...

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Q: 7.A= pVa +qVE +rVc ,B = Va Va-b b. If A=0 prove that, ap + bq + cr' = 3apqr where a be c. If a? = b'...

A: Given that  A=pa3+qb3+rc3 and  B=ab32+ba23 Solution a: a32+abab-b3-aa-b=a32+aba-b-aab-b3ab-b3a-b=a32...

Q: Consider the vectors [1,0,0, -1]; [0, 1, 1, 0]; [1, 1, 1, 1]; [1, 1, 1, 0] (a) Show that they do not...

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Q: Provide a direct proof of the statement below. Let a, b, and c be integers. If a|(a+b), then alb.

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Q: Let n e Z. Prove that n² + 4 is divisible by 8 if and only if 3n + 6 is divisible by 12. (Hint: the ...

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Q: Let f be a function with continuous second derivatives, defined by: z = f (xy, x² + y") If we take u...

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Q: Topic: Complex numbers Instruction: Perform the indicated operations. Express results in rectangular...

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Q: 15с) — Зс2 — сз %3D 3 800 -Зс, + 18с, — бсз 3D 1 200 —4cт — С2 + 12с, 3D 2 350 |

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Q: We are given the following homogenous differential equation and pair of solutions on the given inter...

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Q: Find k such that the function is a probability density function over the given interval. Then write ...

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Q: A patient receives a prescription for 3 g of an antibiotic. The tablets on the shelf are 250 mg. How...

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Q: Find distance between point A(1,3) Perpenclicular the line L: 2y =2+X on

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Q: Let 4 VA v3 %3D vi -2 9. where cER. What is the only value of c for which the set {v1, v2, V3, V4} i...

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Q: Prove Vr, y E Z, if ry is even and y is odd, then r+y is odd.

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Q: J0 t<4 Find L{g(t)} if g(t) =- t2 4

A: The Laplace transform of the function g(t) is represented as G(s) or L[g(t)], it is defined as ∫0∞e-...

Q: (4) Consider the following set: S = {(x, y, z) E R' | xy + yz + x =-2}. (a) Show that S is a surface...

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Q: Give an example of a linear operator TE L(R*") which is not diagonalizable. Justify your answer.

A: give an example of a linear operator T∈Lℝ3,1 which is not diagonalizable. justify ur answer. it is k...

Q: This type of symmetry is a type of balance in which the parts of an object or picture are regularly ...

A: Solution

Q: Matrix B:

A: Given two matrix A and B  ,we have to find the value of A-B.

Q: H.W. Consider that, we have the following linear system X1 - x2 +x3 = 2 + 3x3 = 0 2x1 + 5x2 + x3 = 1...

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Q: Write the following universal statement as an equivalent conditional statement in words. All even nu...

A: We write the given universal statement as an equivalent conditional statement in words. Given statem...

Q: B) Prove that: 1-tan? 0 cos? 0 – sin? 0 1+tan? e

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Q: b) Use the Ratio Test to determine if the series converges diverges. or n5" (2n + 3)ln (n + 1) n=1

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Q: Let y be a solution of the differential equation y = 3, where x > 0, y > 0 2ry such that y(2) = 6 . ...

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Q: Consider the set of vectors in R such that 1223 0. If these form a subspace, show that is satisfies ...

A: See below for solution.

Q: Newton's Method will fail to approximate the solution to f(z) 0 with initial guess ro when: Oco is n...

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Q: Given the surfaces: S : y? = S4 : y + z = 6, S5 x 0, S6 : y = 0, S7 : z = 0. 2x – 4, S2 : x +y = 6, ...

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Q: Let z = axy1 + bx³y*, with a and b constants. P is a point given by (1, 1) and it is known that: dz ...

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Q: Draw the graph of the equation g(x) = –3x +2. You can refer to the section "Drawing Graphs in Mobius...

A: We have to draw a lineggiven by g(x)=-3x + 2.

Q: 2. (a) Detennine the nullity and rank ef the following matrix: 1 10 0 0 0 1 -2 0 4 20 0 3 -2 1 2 2 0...

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Q: prove that the sequence (1/5^n) is convergent and approaches zero?

A: Series and sequences

Q: 5. Use Euler's method with n = 4 to find the approximate value of y(2) if y = 4t – 4y and y(0) = 1. ...

A: Given, f(y,t) = y' = 4t-4yy(0) = 1 and n = 4To find , y(2) So, h = b-an=2-04 = 0.5

Q: A 50 gallon storage tank initially holds a saltwater solution containing 100 grams of salt dissolved...

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Q: A zero coupon bond is a bond that is sold now at a discount and will pay its face value when it matu...

A: Given that: Face value of the bond = $15000 Mature time = 28 years  Buy price = $6000 To determine...

Q: Let U, A, and B be defined as shown below. U ={a, b, c, d, e, f, g, h, i, j } A = { c, d, e, g, i} B...

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Q: Suppose Emerson loses 37% of all checker games. (a) What is the probability that Emerson loses two c...

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Q: Maximise -x² + 0.8x - y² + 1.2y using only points within the sphere a² +y° < 1 What is the value of ...

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Q: Prove by simple induction on n that 2" > n

A: We have to prove 2n&gt;n It is true for n=1

Q: The graph of a conic section is shown below. Identify, among the options, a possible equation for su...

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Q: 1. Solve: ye*) dx + (xe*y+ 2y) dy = 0. %3D 2. Solve: (1+ x²) +y = etanx ty3e" dx %3D 3. Solve: p(p +...

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Q: f(x) = xsinx (-1)"x2n (2n+2)! .2n+2 OA. (-1)"r2n+2 (2n + 1)! O B. n=1 (-1)"x2n+1 (2n+ 1)! C. 1. (-1)...

A: Maclaurain series

Q: Solve (yx-2x^4)p+ (2y^4 - x³y)q = 9z(x? - y^3)

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Q: Let = ary- + ba-y", with a and b constant. Pis a point given by (-1,-1) and it is known that (P) = 2...

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Q: Determine the amplitude, period and displacement for the given function, and sketch the graph of the...

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Q: Let U, A, B, and C be defined as shown below. U= [ a, b, c, d, e, f, g, h, i, j } A = { d, e, g, h, ...

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Q: Let y be a solution of the differential equation y' + !y = -2x°y*, where x > 0, y > 0 such that y(1)...

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Q: A card is randomly drawn from a deck of well-shuffled playing cards. Let event E be that the card is...

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Q: Let Gbe an open set in R". Two points x, Y e G are said to be equivalent if they can be joined by a ...

A: Since every open subset of Rn can be written of countable union of disjoint open balls and each ball...

Q: In a batch of 500 high school students, there are 252 students who own a laptop, 176 students who ow...

A: Here we can use the formula nU = nA+nB-nA∩B+nA∪B'