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

Q: Prove the identity without evaluating the determinant (Using properties). a1 b1+ tai ci+rb1 + sa1|…

A: Use the below properties of the determinant. 1) The determinant remains unaltered if its rows are…

Q: Suppose you estimate to be 0.6 -0.5 0.3 T= 0.3 -0.25 0.15 1.2 -1.0 0.6 a. Show that the determinant…

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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, in which the entries are functions. Determinants of this type occur when…

A: We know that Therefore, value of given determinant is evaluated as follows.

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

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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: 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: 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: Show that y = e", y = e2" , y = x and y = x² are linearly indepent functions %3D Hint: Use the…

A: To show y=ex,y=e2x,y=x,y=x2 are linearly independenr we are going to provethat the workian is…

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: 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: Compute the determinants in Exercises using cofactor expansion alongany row or column that seems…

A: We have to compute the determinant using cofactor expansion along any row: ab00aba0b We know that if…

Q: Linear algebra. please answer part (a)

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

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Q: a;jA = Aô;*, Show that where A is a determinant of order three and A" are cofactors of a.

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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: 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: 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: 7) Show that y = e", y = e", y = x and y r? are linearly indepent functions %3D Hint: Use the…

A: The solution is given as

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

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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: Can cramer's rule be used to solve this %3D 5 or no? IH vesi unith the determinants used to compute…

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Q: Prove the identity without evaluating the determinant (Using properties). a1 b1+ tai c1 + rb1 + sa1…

A: Let,  A=a1a2a3b1b2b3c1c2c3 Now, det A=a1a2a3b1b2b3c1c2c3         ~a1b1c1a2b2c2a3b3c3  (because the…

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

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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: a) ВА b) Determinant of AT c) cofactors(B) Where [3 2 0 0 5 4 7 0 1 A =|1 3 1 0 0 10 3 85 Lo 1 0 1…

A: We have to find the value of (a) BA, (b) determinant of AT and (c) cofactors(B)

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

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Q: Compute the determinants in Exercises using cofactor expansion alongany row or column that seems…

A: Given determinant is: We have to find the value of this determinant.

Q: 63. Use the determinant to determine whether A= [; ] 1 2 is invertible. If it is invertible, compute…

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Q: 3. Prove that |B| = -|A| and identify what property of determinants. -4 1 4 -1 Let A- and B =5 -1 2…

A: To be proved - |B|=-|A| To be mentioned - what property this behavior shows

Q: Let A be a 3-by-3 matrix whose determinant is -5. Use properties of determinants to evaluate the…

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Q: find the values of λ for which the determinant is zero. 2 λ + 1 0 0 1 O(-1, 1, 1) O(-1, 1, 0) O(-1,…

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Q: Express the determant expression of a 3 X 3 matrix using cofactor and minor, Using this, try to…

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

A: Let's find.

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

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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: 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: inition of determinant of T, prove that det(T-¹) = (det(T))−¹ (Hir erminant of the identity man?)

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

A: Let…

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

A: We have to find

Q: Evaluate the determinant by general definition and by Laplace expansion: 2 9 0 1 1 4 6 10 3 -1 1 6.…

A: Suppose we have square matrix as   .The determinant of the matrix is equal to Laplace expansion…