Problem 5. Let det A = 2, det B = 5. Calculate det(A B-ATB). Problem 6....

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Problem 5. Let det A = 2, det B = 5. Calculate det(A B-ATB²). Problem 6. Compute the adjugate of each matrix, and find the inverse of the matrix if it exists: 1 (i) -2 1 [2 1 (i) 1 2 2. 3 -1 4 Problem 7. Use Cramer's Rule to solve the system of linear equations. 2.x1 + 3x2 - x3 =1 x1 + 4.x2 + 2x3 =2 3x1 – x2 - x3 =3 Problem 5. Let det A = 2, det B = 5. Calculate det(A B-ATB²). Problem 6. Compute the adjugate of each matrix, and find the inverse of the matrix if it exists: 1 (i) -2 1 [2 1 (i) 1 2 2. 3 -1 4 Problem 7. Use Cramer's Rule to solve the system of linear equations. 2.x1 + 3x2 - x3 =1 x1 + 4.x2 + 2x3 =2 3x1 – x2 - x3 =3