m427j.homework.6 - M427J Differential Equations 1 Homework Systems of Linear Equations and Matrix Inverses For the following problems solve the

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M427J - Differential Equations Homework 1Systems of Linear Equations and Matrix InversesFor the following problems, solve the given system by writing it as an augmented matrix andreducing the system (i.e., using Gauss-Jordan elimination). Then solve the system by finding thematrix inverseA-1and multiplyingA-1b1.1.2x+ 3y= 23x+ 4y=-11.2.x+y+z= 72x+ 3y+z= 18-x+y-2z= 11.3.x+ 4y+ 3z= 12x+ 8y+ 11z= 7x+ 6y+ 7z= 31.4.y+ 2z= 5x+ 2y+ 5z= 13x+ 2z= 41.5.-3y+z= 02x+y-2z= 23x+ 2y-3z=-11.6.3x-2y+ 6z= 32x-2y+ 5z= 2-4x+ 3y-9z= 41.7.w+y+ 2z= 1x-y-2z= 23w+x-y+ 2z= 1-2w-3z= 21.8.2w+ 4x-y-z=-13w-2x-y-2z= 23w-3x-y-2z=-23w-y-z= 12Homogeneous Linear SystemsSolve the homogeneous systemAx=0(i.e., find the nullspace) for the following matrices.Putyour solution in parametric vector form.2.1.1213-123-812.2.1122243362.3.459-265112348-32.4.3-6902-4723-66-62.5.148-3-7-12734-22955369-5-2
M427J - Differential Equations Homework 3 Determinants Find the determinants of the following matrices. Keep in mind that you can expand across any row