5. Let (image) (a) Compute AB. (b) Compute the determinants of A and B. (c) Is A invertible? (d) Is AB invertible? (Hint: think of one of the properties of determinants).

Q: (a) Use a determinant to find the cross product i × (i + j + k) (b) Check your answer in part (a) by…

A: (a)To find the cross product of i×i+j+k using determinant. Solution: Finding cross product of given…

Q: Let A 1 1 A = 1A -1 1 Then answer the following. (a) Determine a;ı · (a2 x a3), for i = 1, 2, 3. (b)…

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Q: Find the determinant of the matrix. 16

A: The given matrix is: 16

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: Find the determinant of M = (a4-b4)/(a-b) , given that matrix M is:            [ (a+b) (ab) (0) M =…

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Q: Evaluate the following determinants and negative of determinants of order two: (a) (1) 3 4 5 (ii) 3…

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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: Consider the below third order determinant: 3 6 2 1 9 3 2 5 2

A: Determinate of the 3*3 Matrix

Q: 12. Fill in the blanks. The missing word is might, must or cannot. be parallel. te) Two planes…

A: As this is a multiple subpart question, according to the Bartleby answering rule, only first three…

Q: Q4. Using row reduction evaluate the determinant |2 1 3 1| 1 0 1 0 2 1 0 lo 1 1 2 31 And also,…

A: Let ∆=2131101102100123 Applying R1↔R2 , we get  ∆=-1011213102100123 ( on changing any two rows or…

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

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Q: GIVE 2 EXAMPLES FOR THIS THEOREM OF DETERMINANTS Theorem 6: If we express the elements of each row…

A: We will find out the required examples.

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: 3) Find the determinant:erential equation: 1-4 1 41 cos(x) 3 -2 1 1-2 4 16 61

A: The given problem is to find the determinant of the given matrix. Given matrix , [-4 1 4 ; 3 -2 1 ;…

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

A: We have to find determinant

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

A:

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: Show your complete solutions: 1. Using cramer's rule: 2 x1-3 x2 +1.4 x3= -5.2, 1.3 x1 + x2+2.4 x3=…

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Q: Find the determinant of the matrix: 2. 1. 3. Rememberj

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Q: (a) With what sign does the term aina2n-1... and appear in the determinant of the matrix with…

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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: Which of the following is the determinant of the 2 x 2 matrixA= (A) ad-be (B) be- ad (C) (D) ad-bc

A:

Q: Evaluate the determinant of the ナhc given mantrix using 91 92 93 result b2 bz = 5. C3

A: Given that:      a1a2a3b1b2b3c1c2c3=5

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

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Q: 1 5) Let A= 1 -1 TON 0 2 0 -1 3 -6 a) Find A-¹. b) Find det(A), that is, the determinant of A.

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Q: 0 - [1 4 Find the determinant of A = = 1 2 03 -3 8 - using a cofactor expansion.

A: We have to find out determinants

Q: II. Find the determinants or prove the equations in the following. Properties of determinants or…

A: We need to find , determinant of a2 + 2a2a + 112a + 1a + 21331 We will use cofactor method ,  For…

Q: Alsan tet A = and B = 15 [4 101 l7 15J 3 (a) [ Let c 3. Find cA. (b) ts] Find A + B (c) Find the |A|…

A: use property of matrix.

Q: For the matric A find - The Determinant A (|A|). The Co-factor matric of A (Acof). - Where [-4 291…

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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: Let 2 -4 1 -1 1 1 3 -2 A = -3 1 1 1 2 2 -2 -1 1 -2 1 Evaluate the determinant of A.

A: Given a 5×5  matrix. To evaluate the determinant, we keep on reducing the matrix by performing row…