15) Using the properties of determinants or otherwise, show that 1 a² + a²³ 1 a+a²³=0. 1 a a² a³ a+a²

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: Let A = [1 1 2 1 2 -3 5 4 L3 2 -1 1 -1 0 4] 6 and B = a) Find the determinant of A. b) Solve the…

A: Firstly, we will find the determinant by using row operations and then solve the given system of…

Q: 2a₂b₁ Let A = ab₂ + a₂b₁ a₁b3 + a3b₁ a₁b₂+ a₂b₁ 2a₂b₂ a3b₂+ a₂b3 a₁b3 +azb a₂b3+a3b₂. Expressing…

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Q: Consider the fourth-degree polynomial equation a₁ + b₁x²q₁x² + b₂ a₂+ b₂x² a₂x² + b₂ a3 + b3x² a3x²…

A: Given that We know that determinant of a matrix is equal to zero if any two rows or two columns are…

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

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Q: [ab]. C d 6) (i) Compute the adjoint of A= (ii) Show that the determinant of A equals the…

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Q: Using the theorem on determinants, show that 1 a a2 A = 1 b b2 = (b – a)(c – a)(c - b) 11 - с с2

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Q: Find the determinant of S = [321 3 2 0 1 -2 310 1 023 2

A: Matrix given is,

Q: Use the cofactor expansion to compute the following determinant: 5 6 5 det -3 9 7 %3D 6 9-8

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Q: Q2) Compute the value of the determinant by using the Radial method: |2 1 0 D = 1 2 -1 |2 3 4

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Q: Calculating Cross Products with Determinants Find u X v and v X u if u 2i +j + k and v = -4i + 3j +…

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Q: E = F = [2 13 101 1 0210 0 1 2 3 1 -2 0 0 315 3 -7 0 -4 2 010 021 1 001

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Q: 12.) Find the determinant of A= -2 3 1 57 -1 2 0 4 1 0 TN -2 1 3 -3 4 Show your work.

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Q: 2. Use the elimination 2 -3 2 1 -3 2 131 method to evaluate the following determinant. 2 1 -1 -4 23

A: we have to find determinant.

Q: hw bds 1 2 -4 3 2 1 3 -2 -1 -5 1 2 -1 4

A: Given: The matrix is 21-3112-223-43-1-2-1-54. To find: Determinant of the given matrix using the…

Q: 1 Зі -5 A = | ₁/ i

A: Given matrix is A = 13ii-5

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: a a 3. Compute the determinant a a by using the row/column operations a a R, → R, + R, + R, C, →C,-G…

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Q: Use the cofactor expansion to compute the following determinant: -4 8 -7 | det -4 2 6 = 0 0 10 –4

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Q: 12 =[-1²] Let A = @ without using A-1 6 Solve © Solve and B = [ determinants, compute. 24 235 -2 Ax…

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Q: Compute the determinant of A by any method where:

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Q: Compute the determinants using cofactor expansion along the first row and along the first column.

A: Now co factors of first row are

Q: . Solve these two simultaneous linear equations using Cramer's method of determinants.

A: Given,

Q: a. Use cofactor expansion to compute the determinant of A. b. Use elementary row operations to…

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Q: Evaluate the determinant A by any method, |1 3 6 2 1 0 2 |0 A = |3 2 3 0 2 9 5 1 0 10 0 8 6 0 1 2

A: Consider , A = 1310206223302951010086012 We need to find determinant of A. For that we will use ,…

Q: 19 Find the determinants of U and U-¹ and U2. [1 4 6 U = 0 2 5 0 0 3 and b - [8 d U =

A: To find the determinants of U, U-1 and U2. (i) U=146025003 (ii) U=ab0d

Q: Find a 2 x 2 matrix such that 5 1 1 0 2 1

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Q: 1 1 b+c a+c 1 -1 1 a+b+ 111 a b с 0-20 = 0

A: Aim:111b+ca+ca+b1-11+111abc0-20=0