Determinant Form for the Equation of a Line (a) Use the result of Exercise 69(a) to show that the equation of the line containing the points (x1, y1) and (x2, y2) is y 1 1 X2 y2 1 (b) Use the result of part (a) to find an equation for the line containing the points (20, 50) and (-10, 25).

Q: Find u - v, u · u, ||v||², (u - v)v, and u - (3v). u = 4i + j - 2k, v = i - 3j + 2k (a) u: v (b) u.…

A: Dot product of two vector is - a→=  a1i^ +  a2j^ +  a3k^ b→=  bi^ +  b2j^ +  b3k^ a→.b→ =  a1 b1 +…

Q: Find M13 and C13. M13 - C13 = i 39 39 A = -90 0 8 1 0-5 -1 1 -9-2 50 2

A: Given matrix is A = -906-100-5-181-9-21502

Q: We wish to solve the system of linear equations by using Cramer's Rule. Begin by calculating the…

A: given system of equations

Q: Q3) Find the value of x,y from solve these equations by using the Determinants:- 2x + 4y = 10 x – 5y…

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Q: Use properties of determinants to find the value of each determinant if it is known that

A: Given Determinant             x+3y+6z+93u-13v-23w-3123 Decompose given determinant into two…

Q: Q1/ The Volume of box that determinate by A=(-i-3k) , B= (-4j+2i-3k) and C=(8i-3j+2k) ?will be 23…

A: Solved below

Q: |3a, 3b, 3c1 4. 3a, 3b2 3c2 |3az 3b, 3cz - 2аз —2а, аz + Заз| 5. -2b, -2b, b2 + 3b3 -2c3 -2c Cz +…

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Q: Using only the theorems on determinants and the row/column operations, show that: 1 1 a b a² b² 1 C…

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Q: GIVE 2 EXAMPLES FOR THIS THEOREM OF DETERMINANTS Theorem 6: If we express the elements of each row…

A: We will find out the required examples.

Q: A line L, passes through the points A(0, -3, 1) and B(-2,5, 3). (a) (i) Show that AB= 8 6 2 (ii)…

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Q: Find the Jacobian determinant to the test the existence of functional dependence between these three…

A: We have to find the Jacobian determinant of the functions Y1, Y2 and Y3. Here, these are the…

Q: 3) Find the determinant:erential equation: 1-4 1 41 cos(x) 3 -2 1 1-2 4 16 61

A: The given problem is to find the determinant of the given matrix. Given matrix , [-4 1 4 ; 3 -2 1 ;…

Q: 5 1 -2 0 3 0 1 -2 0 4 3 1

A: We have to find determinant

Q: Use properties of determinants to show that the following is an equation of a line through the…

A: Consider the provided matrix, xy1x1y11x2y21=0 Use properties of determinants to show that the…

Q: Let P, Q, R, S be points in the plane. A parallelogram PQRS (where consecutive points are endpoints…

A: To find the area of the parallelogram PQRS using a determinant, we can use the formula  Area…

Q: C. Given the system of equations -3x₂ + 7x3 = 2 x₁ + 2x₂ - x3 = 3 5x₁ - 2x₂ = 2 (a) Compute the…

A: Given the system of equations can be written in matrix form AX=b Let A=0-3712-15-20, X=x1x2x3, b=232…

Q: 2.) Write the solution set of the given homogenous System in parametric vector form. 2x1 + 2x2 + 4x3…

A: We are given the homogeneous system and we have to solve the given system in parametric from.

Q: Work Problem Given the matrix 0 51 0 4 3 A = x+1 0 1 a) Find the values of x for which cofactor…

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Q: b) Using Chio's Condensation Method only in all the steps 7 -7 -5 6. 6. 1 4 11 -8 M = -7 -2 %3D -1 3…

A: M=07-7-5661411-8-70-235-1341-639531Chio's Condensation Method:We have to remove 0 from the a11…

Q: nsider the matrices A = B = 2 C = c- (1 ² 3) 64 69 (a) Calculate AB, BA, AC, BC and (A + B)C. (b)…

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Q: Find the determinant using Gaussian Elimination Methoc 5w + 6x - 5y + 11z = 7 10w + 36x + 10y – 17z…

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Q: Determinar si los ángulos son coterminal 70, 430

A: In trigonometry, two angles in standard position are said to be coterminal if they share the same…

Q: Solve for the 5 -5 4 2 -4 5 1 Г5 -2 3 -3 determinant 5 4 -1 -5 -4 0 4

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Q: 3 4 1 4. 12 24

A: Solution