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Differential Equations and Linear Algebra (4th Edition)
- The determinant of a 22 matrix involves two products. The determinant of a 33 matrix involves six triple products. Show that the determinant of a 44 matrix involves 24 quadruple products.arrow_forwardSolve for the determinant of the following matrix. Show your complete solution.5 -5 4 2 -2 -4 5 -13 5 4 -1 -3 -5 -4 0arrow_forwardIf the determinant of a 4×4 matrix A is det(A)=−5, and the matrix B is obtained from A by swapping the second and fourth columns, thendet(?)=arrow_forward
- If the determinant of the 2x2 matrix 5 a8 b is 7, then what is the determinant of the 2x2 matrix a 5b 8 ?arrow_forwardSuppose you have the following system of equations: 35 x1 + 31 x2 + 12 x3 = 2974 7 x1 + 14 x2 + 27 x3 = 2054 20 x1 + 13 x2 + 14 x3 = 1830 a. Convert this system of equations in the matrix form and calculate the determinant of the coefficient matrix. What is the determinant of the coefficient matrix? b. Take the coefficient matrix, and calculate its co-factors, and the adjoint. Use the adjoint to invert the matrix. Use inverse of the coefficient matrix to solve the system of equations. Right now, enter the following values: c. What is the value of c13 , c23 , C32 ? d. What is the value of x1? x2, x3?arrow_forwardIf X = (25 -10 ) and Y = (31 -1-2 ) Find: a. YX b. determinant X c. Adjoint Y d. X-1arrow_forward
- Given the following matrix: B = a b c c d e f g h Let's say that det(A) = −6. Let B be another 3 × 3 matrix (which is not given here) with det(B) = 6. How could you find the determinant of the following matrices? D = 5A^-1B^Tarrow_forwardFor the matrix A = 0 5 8 Cofactor C21? 4 5 2 9 4 4arrow_forwardIf the determinant of a 3×3 matrix A is det(A)=2, and the matrix B is obtained from A by multiplying the first column by 3, thendet(B)=arrow_forward
- Find the determinant of the following matrix5 -2 3 0 4 23 3 4arrow_forwardFind the determinant of the matrix, if it exists. (If an answer does not exist, enter DNE.) -5 0 2 -9arrow_forwardIf the determinant of a 5×5 matrix A is det(A)=8, and the matrix C is obtained from A by swapping the third and fourth rows, thendet(?)=arrow_forward
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