Q3/A/ If ā = i – 2j + k , b = i + 2j – 4k and č = 2i – 3j + k Find: i) (ā x b). (ā x c) ii) (ā x b) × (ā x c)

Q: (b) ruz – 2yuy + u = eª , for x> 0

A: 1.(b) Given partial differential equation xux-2yuy+u=ex, for x>0 This can be written as…

Q: Find the real valued general solution of y" + 5y = 0. %3D

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Q: Solve by using Cramer's rule: z+ 3x = 1 y + x - z = 2 X – y = 3

A: Cramer's rule in brief: find the determinant of the matrix formed by the coefficients of variables…

Q: 3. JX)=3X - g(x)=35x-30X+3 are ortnogonai each ther on [-1, 1].

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Q: Use Cramer’s Rule to solve x + 6y − 4z = 10 4x − y − 3z = −8 x + y − 2z = 7

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Q: 4. By using Cramer's rule, find the value óf Y: 2x +3y-2=16 5X-y +2Z = 36 X + 2y -42 =5

A: We have given that  2x+3y-z=16 5x-y+2z=36 x+2y-4z=5       In matrix form  23-15-1   212-4xyz=16365…

Q: To the reci max z Ax1 +B x2 A=6 s.t. 2x +4x 2 12, B=1 -X1 + 2x2 S 2, X1 20, x2 Free.

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Q: Use the IVT to prove that r-5x2 + 2x = -1 has a solution. %3D

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Q: What is the particular solution for y′=−2e^x−3x^2+x−4 such that y(0)=1?

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Q: use Cramers rule to Solve for y only. 2x-44-32 = 4 %3D -3x+2y+52=-5

A: Please see the below picture for detailed solution.

Q: Solve this problem using the indeterminate coefficients method: y" +2y' + y = 2cos(2x)+3x+2+3e^x

A: Given: y"+2y'+y=2cos(2x)+3x+2+3ex

Q: Axk + 2xk + k +1 = xk+1 + xk + k +1 = 0. cion to the last equation is %3D

A: Given, let the function f be equal to△yk2; therefore, equation (6.52) becomes…

Q: Evaluate 6(4z² +10z+1)dz, where C is drawn in the figure 2i 2

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Q: Verify that y, = e2x and y2 = e5×are solutions of у" - 7у' + 10у %3D 0

A: We have to verify that the functions y1=e2x and y2=e5x are solutions to the given differential…

Q: Solve the equation 2x+y-z=1,x-y+z=2,5x+5y-4z=3 by Cramers rule

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Q: Use Cramer's rule find yhe solution of x1: 2x1+X2-3x3=0 4x1+5x2+X3=8 -2x1-x+4x3=2

A: write the matrix D from the given equations  D=21-3451-2-14 calculate the determinant D…

Q: Find abs. max 8 min f(xeg) = x²-3y² - 2x + 6y | on R: square which vertices Coc0)r (200] (2ィ2),(o/2)

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Q: V1-y² -1 0 kpxpzp (,x + zA),I „«-,S

A: The given integral is: I=∫-11∫01-y2∫0x y2+x2 dz dx dy

Q: z² - xy = 2 at the point (2, 1)= %3D

A: We have to find the slope of the line tangent  to the given curve.

Q: 2t + 3 r(t) -, In(t² + 2) t2 +1

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Q: Q2: Use Cramer's rule to solve 3x, - 0.1x2 0.2x, = 7.85 0.1x, + 7x2 - 0.3x3 = -19.3 0.3x - 0.2x, +…

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Q: B. Use Cramer's Rule to find the solution to 2x1 + x2 + x3 = 2x1 – 3x2 – 3x3 = 3 - - -2x1 – 2x2 +…

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Q: 4. Find for the particular solution of y' = x3 – 2xy when x = 1, y = 2 %3D

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Q: Solve using Cramer's Rule only. 4w + 3x – 5y + z = 58 6w – 5x + 2y+ 2z -9w + 9x + 6y + 3z = 6 3w +…

A: This is a problem of system of linear equation. Please follow the procedure given below for cramer's…

Q: Q1 : Find the solution of x, y, z by using Gramer's Rule. 3x + 2y – z = 1 x - y + 5z = -2 2x + y = 3

A: As per our guidelines we need to solve only one question. Please repost the remaining questions as…

Q: b) Find particular solution of х*у %3D- (х* - 1) у, У(1) %3D 1.

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Q: Мaximize 2 3 4х + 4y || 3x + 7y < 63 6x + 2y < 54 Subject to Маximum is at y = VI ALAL II

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Q: 5. Find the second solution by reduction of order method: (1- 2x? y" + 4xy' – 4y=0 y, (x)=-2x

A: Differential equation and it's solution

Q: II. Verify that ду дх дх ду 3 2 2. f(x, у) %3Dх'у? — ху 'y² – xy ³

A: Given function: Now,

Q: Solve using Cramer's Rule: (2x z = 14 3x - y + 5z = 0 4x +2y + 3z = -2

A: The equation can be expressed as 2x+0y-z-14=03x-y+5z+0=04x+2y+3z+2=0use Cramer's rule to find the…

Q: 7x-4y-3z = 21 -4x+7y-z = 0 -3x-y+5z = 0 x, y, z?

A: Given

Q: Find the general solution of (3D2 + 5DD' - 2D'2)Z = 10 cosh(2x + 5y).

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Q: 2- Show that: 2 J1(x) = (-1)m x2m+ (2m + 1)! m=0

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Q: 6y" – 7y' – 5y = 2x³ + e¯* – 5 -

A: Ordinary differential equation involves the derivative of single dependent and single independent…

Q: Use Cramer’s rule to solve for x 2x=3y-4z+11 9x+y=z-1 3x-4y=7

A: Given,

Q: gona u = 2i – 3 j+5k v= 4i -9j-7k

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Q: Use Cramer's rule and solve 6x-4z=26 7x+8y+5z=122 9x-9y=54

A: Use Cramer’srule and solve.

Q: az (b) Solve and ди by applying chain rule if z = In(x² – 2y), and x = u + v, y = e". dv

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Q: Solve using Cramer's Rule only. 4w + 3x – 5y + z = 6w – 5x + 2y+ 2z -9w + 9x + 6y + 3z = 6 3w + x +…

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Q: 11 sec²(3t), 0 < t C₁ and C₂ as arbitrar

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Q: Solve the equation using Cramer's Rule. 3x + y + 2z = 5 x + 3z - 3y =2 2x + 3y -z = 1

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Q: Use Cramer’s Rule to solve:…

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Q: 4. Determine the unknowns using [X] = [A]¯*[B] and [A] by the adjoint method. %3D 10x + 2y – z = 27…

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Q: Verify that y = ODE y" + 3y' + 2y = 4x². -4e-x-2e-2x + 2x² - 6x +7 is a solution of the SHOW ALL…

A: We have to verify that y=-4e-x-2e-2x+2x2-6x+7 is a solution of the ordinary differential equation…

Q: If x &lt; 0 and y &gt; 0, determine the sign of the realnumber. xy

A: Let x&lt;0 and y&gt;0

Q: Use Cramer's rule to solve the simultaneous equations 2x + y = 7 3x – 4y = 5

A: The equations can be expressed as 2x+y-7=03x-4y-5=0

Q: Irr( V1 + 7, Q) = Vī, Q) = O gt – 4x² – 2 O xt – x - None O xt – 2x² – 6

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Q: 3a Show that the method xn+1 = Xn 6+ Xn ,converage to vā. %3D a

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