Use a determinant to find an equation of the plane passing through the points. (0, 0, 0), (1, 0, 3), (0, 3, 2) 5x + 9y – z= 0

Q: 2 -1 1 -1 1 A = -1 3 1 -1 3 2 -1

A: Given

Q: Using the property of determinants, prove that |1 bc a(b+c)| 1 1 ab c(a+ b)| 2) ca b(c +a)| = 0

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Q: Compute the determinant using a cofactor expansion down the first column. 1 -5 A= 8 3 4 -2

A: It is required to determine the determinant of the given matrix using a cofactor expansion down the…

Q: 2. Use row/column operations and properties of determinants to show that (Do not expand using…

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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: Use expansion by cofactors to find the determinant of the matrix. y 30 -27 18 24 -10 32 -18 24 -40…

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Q: Find determinant of the matrix using row or column operations and properties of the determinants…

A: Determinant of matrix

Q: Find the determinant of the matrix. Expand by cofactors using the indicated row or column. |-2 5 3 3…

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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: a) By using the property of the determinants prove that 1 + a? - b2 2ab -2b 1- a? + b? = (1 + a? +…

A: By using the properity of determinats prove that :

Q: Evaluate the determinants to verify the equation.

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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: 3] Use determinants to find the values of X, Y, Z, W, M. 26 14X7Y+5Z - 11W + 21M = 33 -3X + 5Y-13Z -…

A: We have to find the values of X, Y, Z, W, and M using determinants.

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: 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: Let a, b e R. (a) Find the determinant of -2 1 -2 - 2.

A: (a) Given that, a2b-2124-2-1

Q: (a) Find x, y, z and B, where [0 x 37 A= 1 -3 y; A² = 1; c(4+1) + 3B7 = 2A and I: unit matrix 4 4…

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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: Find the determinants of the following matrices and classify them as either singular or non…

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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 formula for the area of a triangle to find the area of the triangle in the…

A: Here, x1y1, x2y2, x3y3 are 31, -13, -2-2

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

A:

Q: 3] Use determinants to find the values of X, Y, Z, W, N. 8X - 3Y + Z + 5W – 4N = 21 5X + Y + 7Z -…

A: We have: 8X-3Y+Z+5W-4N=215X+Y+7Z-13W+15N=277X+3Y+4Z-18W-12N=3511X-7Y-Z+9W+15N=5015X+10Y-7Z+2W+8N=19…

Q: Find the value of the determinant using lhe Following mettiods: W Laphace Expan sion 4 %3D 3. 6 2 2.…

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Q: Describe the determinants D, Dx, and D, in terms of the coefficients and constants in a system of…

A: Consider the system of two equations in two variables as follows: a1x+b1y=c1a2x+b2y=c2 By using…

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

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

A: (x,y)      two points given that (-2,5)     &      (4,3)

Q: 10 0 o U21 210 N -001 1120 II

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Q: Use expansion by cofactors to find the determinant of the matrix. y 21 -18 30 27 -32 18 -24 10 -22…

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Q: Using the properties of determinants, prove that : 1 1 1 = (a – b)(b - c)(c - a)(a + b + c) a' b' c'

A: The solution to the given question is explained below.

Q: A = 4 2 2 5 2. N 23 1

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Q: Find the values of 1 for which the determinant is zero. (Enter your answers as a comma-separated…

A: finding determinant by using first column

Q: -2 3 11 4 5 -3 4 -2

A: We need to find the Determinant.  Now, consider:…

Q: [W -X -W | X R = y W -X y Z y y

A: Let's find.

Q: Find the determinant of the matrix. Expand by cofactors using the indicated row or column. 5 5 |-4 5…

A: Using properties of determinant to find determinant of the matrix.

Q: Use expansion by cofactors to find the determinant of the matrix.

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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: 2. Use row/column operations and properties of determinants to show that (Do not expand using…

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Q: For the matric A find - The Determinant A (|A|). The Co-factor matric of A (Acof). Where T-4 2 -9]…

A: Given :A=-42-93411-32

Q: Calculate:  a) AB b) A’D’B’ c) Find the determinant of D. Show all work

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Q: Find the values of λ for which the determinant is zero.

A: Given: λ+221λ for finding value of λ, where given determinant is zero we expand given determinant…

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: 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: Use a determinant to find an equation of the plane passing through the points.(0, 0, 0), (2, −1, 1),…

A: we know that equation of plane passing through pointsx1,y1, x2,y2, x3,y3 is given by…

Q: Evaluate the determinants to verify the equation.

A: Given: wxyz=wx+cwyz+cy

Q: Show that the equation of a line through (x1, yı) and (x2, y2) is given by the following…

A: A determinant

Q: Use matrix determinant method to solve for, A*B*C where; A=(0.64i+0.768j+0k) B=(1.5i+1.8j+1.6k)…

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