2. Use row/column operations and properties of determinants to show that (Do not expand using cofactors) 1 1 1 (b – a)(c – a)(c – b) a a2 62 c2

Q: |1 a а2 A = |1 b b² b b23 (b — а)(с - а)(с — b) %3D c2

A:

Q: 1 3 -1] 3 2 X = ,A = 5 2 6 4 -4 5 -3,E || 3 -4 1 1 2 [ 3 2 6 1

A: Given: To find the value of k by finding the determinants using a co-factors technique, then the…

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: Evaluate the determinant by general definition k 1 1 1 1 k 11 k 1

A: Here qe have to solve the determinant

Q: Suppose A is a 2x2 invertible Martix. Is the following statement true or false?  The determinant a A…

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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: Using the theorem on determinants, show that |1 а a? b b2 = (b – a)(c – a)(c – b) c2 A = 1 %3D

A:

Q: 1.3.6 Show that the multiplicative property of determinants gives the real four- square identity (af…

A: To show: The multiplicative property of determinants gives the real four square identity: -…

Q: Using the theorem on determinants, show that a a? b b2 1 |1 A = 1 (b – a)(c – a)(c – b) - C

A: We have to show that A=1aa21bb21cc2=(b-a)(c-a)(c-b) by using the theorem on determinants .

Q: 1 3 Using properties of determinants, show that 2 -3 =0 8 3 21 139

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Q: 1 3 1 Using properties of determinants, show that 2 3 8 - 3 = 0 %3D 21 9

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Q: Solve for the determinant using Cofactor Expansion Method only. 1 3 5 1 4 3 7 A = 2 4 6 8 5 7 3 6 7…

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Q: Use the fact that |cA| = c|A| to evaluate the determinant of the n x n matrix. 24 12 36 A = 20 32 16…

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Q: 2. Find the determinant [1 a) A = 2 -1 1 Lo %3D 1 -1 23

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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

A:

Q: Using the theorem on determinants, show that |1 a2 a A 1 (ь — а) (с — а)(с — b) b b2 | - c²

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Q: 2а 2b b - c 2b 2а а+c| %3D-2(а — b)?(а + b) а +b a+ b а

A: This is a determinant problem

Q: 3 ) Using properties of determinants, show that 2 3 21

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Q: 2. Let B = {v₁ =, √₂ =, V3 =, V4 =}. Use determinant to determine whether B is linearly independent…

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Q: Using the theorem on determinants, show that a² |1 A = а b b2 (b – a)(c – a)(c – b) 1 c2

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Q: Use cofactor expansions to evaluate the determinant. Expand along the row or column that minimizes…

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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: 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: |1 3 Using properties of determinants, show that 2 -1 - 3 =0 3 21 -9|

A:

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: (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 the method of elementary operations to evaluate the determinant 2 -4 3 6. 1 2 -2 3 -5 4 -4 -2 3…

A: To find- Use the method of elementary operations to evaluate the determinant 2-43612-23-54-4-23734…

Q: Linear algebra

A:

Q: Evaluate the determinant, using row or column operations whenever possible to simplify your work.

A: 1234502468003690004800005

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

A:

Q: |1 3 Using properties of determinants, show that 2 3 21 8 -3 =0

A: Consider the determinant, 13-128-3321-9=0

Q: Q.1 (a) Evaluate the determinant without ex pansion by using minimum number of operations. 1 a a a?…

A: To use simple determinant property to solve the given problem

Q: Using the theorem on determinants, show that 11 а а- А %3D |1 b b2| %3D (b — а)(с — а)(с - b) с с2

A:

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: Evaluate the determinant of A by using elimination method. 20 3 2 5 1 2 4 3 0 1 2 A = 5 3 2 1

A: Given: A=2032512430125321 Applying R2→R2-52R1, R3→R3-32R1,  R4→R4-52R1 Then the matrix A reduces to…

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: 5. Use J the evaluate 9 5 matrix capabilities graphing the determinant: utility to -5 0 CH 3 6 3

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Q: [2 3 What is the determinant of the product of matrices A: and |3D 0 1 -17 B = 2 1 Artivat 2.

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Q: Using the property of determinants, prove that |24 18 30| 1) 2 1 17 = 0 4 3

A: We need to prove that                         .

Q: Compute the determinant of the matrix A, below, by using row operations to transform the determinant…

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Q: Evaluate the determinant, in which the entries are functions. Determinants of this type occur when…

A: Given 3x4lnx34x. The objective is to evaluate the determinant.

Q: 0 30 0 3 5 7 0 1. Let A = Using cofactor expansions, compute the determinant of A. 6 8 4 2 0 9 5 0

A: Just expand using first row.

Q: By calculating AB and evaluating the determinants, verify that det AB = det A det B a12 b12 for the…

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Q: Use reduction to triangular form to evaluate the determinant of the given matrix. 1 A = 3 16 24 0-1…

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Q: Use the fact that |cA| = c^|A| to evaluate the determinant of the n × n matrix. 12 3 27 A = 15 9 18…

A: To evaluate the determinant of the matrix A, by using the fact cA=cnA.A=123271591824621

Q: 1 3 3 2 X = 2 4 ,A = |-4 5 -3,B %3D I-3 -4 5 -1 1 2 3 2 6. = |-4 5 -3 -1 1 Find the value of K by…

A: If a matrix is defined as: A=abcdefghi Then the determinant of the matrix A is:…

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

A: Let…

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: 1. Use your knowledge of how elementary row operations affect determinants to find the determinant…

A: Follow the steps to reduce into echelon form. Operate only rows not coloumns.

Q: Explain why the statement is true, or give a counter-example: If we know that A is a square matrix…

A: Given that A is any square matrix and A=QR be its decomposition.