If the coordinates of a triangle are given, then, its area may be solved using the formula 1 |X1 Y₁ Area of triangle = = X2 Y2 X3 Y3 1| 111 2 Note: This formula requires the sequence of the points to be in counterclockwise manner. Find the area of the triangle (use Laplace cofactor expansion for the determinant) formed by the intersections of the lines: 2x + 3y - 160 x-y-3=0 7x-2y-6=0 Use Cramer's Rule in finding the points of intersection.

Q: Use Cramer's rule to solve the following equations I-y+:=1 2r +:= 2 3r+y-3: 3

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Q: In a mass spring damper system, the acceleration, a m/s², velocity, v m/s and displacement, s m are…

A: cramer's rule to find solution of linear equation of 3 variable…

Q: Find the cross-product of M x N.  Tip: use the determinant

A: Given M=2(ρsinϕcosϕ+ρcosϕsinϕ)ρ+2(-ρsin2ϕ+ρcos2ϕ)ϕ+zz and N=2ρ2cosϕρ+2ρ2sinϕϕ

Q: 3. Solve the system below using the specified method. Write your answer in vector form. X1 - 3x2 = 2…

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Q: Evaluate ( 3+j4)( 3+j4) = A +jB, determine the real component A

A: Given,              (3+j4)(3+j4)=A+jB

Q: 2. Determine the equation of the following function. State your answer as a piecewise function. y 10…

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Q: Solve the following equation byCramer's rule and find the value ofx, y, z. 3x + y + z = 3, 2x + 2y +…

A: The given equations can be expressed as ,  3x + y + z - 3= 02x+2y + 5z + 1 = 0x - 3y - 4z - 2 = 0 We…

Q: Given a generic 2x2 matrix A, and a second 2x2 matrix C, show the following: d. Using property c…

A: In this question, concept of matrix operation is applied. Matrix  A matrix is a rectangular array…

Q: Find the determinant of the vector A = 2i+ 5j + 6k and B = 8k

A: determinant is nothing but finding the cross product. so, determinant of two vectors A and B = A×B

Q: Find the cross product a x b. a = j + 6k, b = 3i - j + 5k Verify that it is orthogonal to both a and…

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Q: 2x-y 2 2 + y+3x 3 2 =1

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Q: Solve the initial value problem below using the method of Laplace transforms. y" - 4y' - 12y = 0,…

A: Given equation is: y"-4y'-12y=0 ,y(0)=1,y'(0)=38 We have to find the value of y(x)

Q: Solve for the value of x, y, and z using Cramer's Rule 8x +15y + 3z = 143 3x - 7y + 13zi = -62 +…

A: We will find out the required solution using Cramer's rule.

Q: give vector form for the solution

A: Here we have to find the vector form

Q: Suppose A = 4i-6j, B = i + 7j, and C = 9i - 5j. Then the scalars h and k such that A = hB+ kC are…

A: Topic = Vector

Q: The vector equations of the two lines are r1={5-6}+t{3 1) and r2={4 1}+p{-2 3}. Determin the points…

A: To find the intersection point of vector equations: r1 =(5, -6)+t(3, 1) and r2=(4, 1)+p(-2, 3).

Q: Divide the quaternion on the right 5 + 4i− 6j  of the quaternion 3i+j-2k

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Q: If u = 2i + 5j; v = i - 2j; w = 3i - j, so u + v * w is:   -3   3   6 -6  9

A: Given that: u = 2i + 5jv = i - 2jw = 3i - j To find: u + vw

Q: Given u = - i+j, v = 10i-4j, and w= -8j, find proju (v + w).

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Q: Compute the order of each element in the Quaternions, Q8. Show your work.

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Q: B: Find the values x,y, and z in the following linear equations by using Cramer's rule: x + 2y =…

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