Suppose (x, y, z) and (1, 1, 0) and (1, 2, 1) lie on a plane through the origin. What determinant is zero? What equation does this give for the plane?

Q: Compute the determinants using cofactor expansion along any row or column that seems convenient

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Q: Let A be an n × n nonzero matrix satisfying A10 = O. Explain why A must be singular. What properties…

A: Here given

Q: Use the determinant version of the cross product to compute u X v.

A: The given vectors are u=011, and  v=3-12 The objective is to find the cross product of the vectors u…

Q: Find a 2 * 2 determinant formula for the area of the triangle in the xy-plane with vertices at (0,…

A: Given, vertices of the triangle are

Q: Prove that a 3 by 3 determinant in which the entries in column 1 equal those in column 3 has the…

A: We know that the value of a determinant with any two identical rows or any two identical columns is…

Q: The scalar  equation of the plane passes through (-1, 3, -2), (-1, 2, -1) and (4, 1, -2) is:   a.…

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Q: Use only column interganges od row interchanges to produce a triangular determinant and find the…

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Q: Use a determinant to find an equation of the plane passing through the points. (0, 0, 0), (1, 0, 3),…

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Q: Use expansion by cofactors to find the determinant of the matri: 4 20 0 6 0 1 2 4 5 0 0 35 4 0 0 6 3…

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Q: (4) Use determinant to find the area of the triangle with vertices (0, 0), (x1,Yı), and (x2, Y2) in…

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Q: Let p = (-1, 2, 5) and q = (4,0, -3) . By using determinant notation for the points give cross…

A: Given- p=-1,2,5 and q= 4,0,3 To Check- The cross product of p×q is equal to -6i+17j-8k.

Q: Use a determinant to find an equation of the line passing through the points (1, 4) and (5, −2).

A: Let (x, y) be any point on the line passing through given points.

Q: 1.What is the definition of the cross product?2. How is the determinant of a 3 × 3 matrix used in…

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Q: Use the determinant to find the equation of a plane passing through the points (3, 2, -2), (3, -2,…

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Q: I'm confused about how we calculate the area of a parallelogram determined by the points (-2,-2),…

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Q: What is the determinant formula for calculating the cross product of two vectors relative to the…

A: Consider two vectors relative to the Cartesian i, j, k-coordinate system.

Q: 2. Use determinants to calculate the area of the triangle with vertices (-1,2), (5,-3), and (4,4).

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Q: Find the determinant. W(x5, x²) = fot 2x = (x²)(5x4)-(2x)(x5) The Wronskian ---Select--- equal to 0…

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Q: what is the relationship between the det(CA) and det(A) if the size of A is nxn? list the properties…

A: Properties of Determinants:·  Let A be an n × n  matrix and c be a scalar then:·  Suppose that A, B,…

Q: The velocity of a car, accelerating at uniform acceleration a between two points, is given by v = u…

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Q: Use the determinant version of the cross product to compute u X v.

A: Given vectors: u=3-12,  v=011

Q: c. Given that the vector à = a,î + azĵ + azk and b = b,î + b2ĵ + bzk. Show that the vector product…

A: Given:     a→=a1i+a2j+a3k     b→=b1i+b2j+b3k  The vector product of two vectors  a→=a1i+a2j+a3k and…

Q: Use the determinant version of the cross product to compute u X v.

A: Solution: Consider the two vectors a = a1i + a2j + a3k and b = b1i + b2j + b3k and their cross…

Q: Find a 3 x 3 determinant equation similar to that in Exercise 7 that describes the equation of the…

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Q: For three points on the plane (x1, y1), (x2, y2) and (x3, y3) show that the determinant of | x1 y1 1…

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Q: [2 1 -1 3. 2. Encuentre el determinante de la matriz B = llevándola a la forma escalonada y -2 1 [3…

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Q: Find a concise 3 * 3 determinant formula that gives the area of a triangle in the xy-plane having…

A: To determine the determinant formula that gives the area of a triangle.

Q: By computing the determinant of a suitable 3 x 3 matrix, find the volume of the parallelepiped with…

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Q: Use a determinant to find the area of the parallelogram with the given vertices. (0, 0), (2, 0), (2,…

A: On solving , we get

Q: Use a determinant to find an equation of the line passing through the points.(−4, 0), (4, 4)

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

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Q: Sketch the triangle with the given vertices, and use a determinant to find its area. (-2, 5), (7,…

A: Given that: Points are-  (-2, 5), (7, 2), (3, -4)

Q: Compute the determinants using cofactor expansion along any row or column that seems convenient

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Q: Why Wronskian determinant W(a) = |X(a)| is nonzero?

A: A Wronskian is a mathematical tool that is used to check for linear independence of solutions of…

Q: Find the equation of the plane that contains the point (2, 1, 6) and is perpendicular to the two…

A: We need to determine the equation of the plane that contains the point: 2, 1, 6 and is perpendicular…

Q: Use the theorem for three linearly independent vectors (that is, calculate a determinant) to…

A: Here it is given that u ,v ,w  Find it is u, v, and w are linearly dependent or independent.

Q: Starting from Cartesian coordinates described in terms of cylindrical coordi- nates, use the…

A: We will show the following result using Jacobian determinant.

Q: Compute the determinant of 1 1 2 3 A = -1 -1 0 -1 -2 3 by using row operations to obtain upper…

A: Given, A=12100123-20-1-1300-1

Q: Sketch the triangle with the given vertices, and use a determinant to find its area. (-1, 3), (2,…

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Q: Let B={V₁ =,2 =, V3 =}. Use determinant to determine whether B is linearly independent or linearly…

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Q: Use a determinant to find an equation of the line passing through the points.(2, 5), (6, −1)

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Q: Find the determinant of the vectors (2,4,0),(0,4,6),(8,0,6) with respect to the base…

A: Let  S = (2 4 0), ( 0 4 6) , (8 0 6)                      α1          α2          α3&      T =…

Q: 1. Encuentre la ecuación del plano determinado por los puntos P(1,2,3) Q(2,3,1) R(0,-2,-1) 2.…

A: Vector equation of the plane passing through the three points with position vectors a, b and c is…

Q: Use the determinant version of the cross product to compute. u X v.

A: Let two vectors u and v: u=u1, u2, u3v=v1, v2, v3 For cross product of these two vector by…

Q: ketch the triangle with vertices (3/2, 0), (2, 6), (1, 4) and use a determinate to find its area.

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Q: Use a determinant to find an equation of the plane passing through the points.(0, 0, 0), (1, 0, 3),…

A: Consider the following points: 0,0,0, 1,0,3, 0,3,4 x1=0,y1=0,z1=0x2=1,y2=0,z2=3x3=0,y3=3,z3=4

Q: Ja + b а а a + b — b? (За + b) а а %3D а а + bl а

A: Let…

Q: 1 - 2 0 3 - 5 2 A = 1 1 -1 2 3 4 2 1 3.

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Q: Using only the theorems on determinants and the row/column operations, show that: 0 0 0 0 5 0 0 0 2…

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Q: Find the vector, not with determinants, but by using propertles of cross products. (1 x ]) x k Watch…

A: Cross products property i x j = k           eq(1) j x k= i k x i= j And i x i=0 , j x j=0 and k x…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.