Question 1(a) Find the solution of the equations by the use of determinants (Cramer's Rule): 2x+3y+2=0 3x+4y+6=0 1 1 1 Question 1(b) Factorize a b C a b c² Question 2(a) Find the inverse of the matrix A = (10) (20) (( 4 by adjoint method. (10) 2 0 1 determine the eigenvalues of the. -12 0 Question 2(b) If Ax=x, where A= -1 4-1 matrix A and an eigenvector corresponding to any one eigenvalue. (25) 2 9 Question 3(a) Given that A= 6 0 4 15-3 and 8 0: find A.B and B.A (15) -4 7) Question 3(b) Solve the set of equations by Gaussian elimination method I x-4y-2z=21 2x+y+2z = 3 3x + 2y z=-2 d States) Text Predictions: On Accessibility: Unavailable DELL (20) Focu

Q: 2 1 0-2 -1 0 -1 1 2 0 1 2 1 0 along the fourth column 3

A: Here we have to calculate the determinant value of the given matrix.

Q: (a) det(A-1) (b) det(5A)

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Q: Find the RREF of the matrix -4 1 -3 من که من 2 3 -1 4 -2 3 2

A: to find the row reduced echelon form of -4       31      - 1-3       42       - 23        2

Q: Determine the determinant of the matrix A det(A) = 1 -5 -1 2 -1 2 5 2 -1

A: The determinant of the matrix A=12-1-5-12-152 is…

Q: ) Solve the system using Cramer's Rule. x 4x + 9y = + 6y = -3 1 First, write the system as a matrix…

A: Consider the system

Q: -3 0 -1 0 -1 0 Find the eigenvalues and an orthonormal basis for each eigenspace. A₁ = -1 0 The…

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Q: Find the determinant of the matrix -3 5 6] M = 0 -1 8 0 0 3 det (M) =

A: Here we have to find the determinant of the given Matrix MThe solution is given below

Q: Consider the matrix 1 2 A = 1 3 4 -3 8. (a) Is A invertible? If so, compute its inverse. If not,…

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Q: Find the determinants of the given matrice A= (9) A = 9 1.

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Q: 3. Let D, E and F be 4x4 matrices such that det (D) = 2, det (E) = 3, and det (F) = 4. Calculate the…

A: For square matrices A and B of order nXn. The following properties hold. det(kA)=kn det(A).     For…

Q: Evaluate the determinant of the given matrix. det(A) = A² + 3x + 12 A²+ 3A - 10 x² + 3x + 2 A²+ 3A -…

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Q: (a) Calculate the determinant 0 1 2 -1 1 0 20 3 (b) Hence, or otherwise, state whether the following…

A: (a)  Given matrix determinant is  012-110203 =0 - 1-3-0+20-2…