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- 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.In this Problems first calculate the operational determinant of the given system in order to determine how many arbitrary constants should appear in a general solution. Then attempt to solve the system explicitly so as to find such a general solution (D2+ 1)x + (D2 - 2)y = 2e-t (D2 - 1)x+ D2y = 012. Why does working with a special linear system (i.e. an n by n linear system of equations whose coefficient matrix has determinant 1) easier to work with through the lens of applying Cramer's rule to solve this system. IN CONCISE SIMPLE TERMS
- Solve the system ax - by + 2cz = -4, ax + 3by - cz = 1 and 2ax + by + 3cz = 2 for (x, y, z) in terms of the nonzero constants a, b, and c.If the determinant of the coeffhcient matrix of a system of linear equations is very small compared to its entries, then the system is said to be _____Find the solution of the given system of equations using Cramer's Rule. Note: these problems are very similar to problems from earlier sections and you can always check your answer using any of those methods. If the system has no unique solution, enter NOT INDEPENDENT. x + y = 26 x−y = 4
- You are given the following matrix: [0 1 2] [-1 1 0][2 0 3] What is the determinant?The equation for a straight line (deterministic model) is y=β0+β1x. If the line passes through the point (−5,5), then x=−5, y=5 must satisfy the equation; that is, 5=β0+β1(−5). Similarly, if the line passes through the point (2,11), then x=2, y=11 must satisfy the equation; that is, 11=β0+β1(2). Use these two equations to solve for β0 and β1; then find the equation of the line that passes through the points (−5,5) and (2,11). Find β0 and β1. β1=enter your response here β0=enter your response here (Simplify your answers. Type integers or simplified fractions.)Find the solution of the given system of equations using Cramer's Rule. Note: these problems are very similar to problems from earlier sections and you can always check your answer using any of those methods. If the system has no unique solution, enter NOT INDEPENDENT. 6x + y = 16 −6x + y = 16