Write the given system in the matrix form x' = Ax + f. dx -=t³x-y-z+t . = etz - 2 =tx-y+9z-e¹ dy dt dt Express the given system in matrix form.

Write the given second order equation as its equivalent system of first order equations. u" + 5u' + 7u = 0 Use v to represent the "velocity function", i.e. v = Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) u'(t). u' = Now write the system using matrices: u d dt V

Compute the matrix exponential eat for the system x' = Ax given below. x₁ = 41x₁40x2, x 2 = 38x₁ - 37x2 1 eAt (Use integers or fractions for any numbers in the expression.)

2x+y+z=7 4x−3y+2z=4 3x+2y−2z=5 Write the system in matrix form Ax=B. Determine the inverse matrix A−1. Use the inverse matrix to find the solution vector x.

Consider the system of linear equations given by:2x1+ x2− 3x3=8−x2​+ 2x3​=−4 9x1​+ 4x2​− x3​=9 Write the system in matrix form Ax=B. Calculate the determinant of matrix A (∣A∣)