We are not using calculator so the steps need to be shown to the solution.
1) The augmented matrix of a linear system has been transformed by row operations into the form below. Determine if the system is consistent.
2x - y = 7, x + 4y = -5

A system is defined by the equations:
x1 = -3x1 + 2x2 + x3 + 2u1 + u2
x2 = 3x1 - 2x2 + x3 + u1
x3 = -4x2 - x3 + u1
y1 = 5x1 - 3x2 + x3 + u1
y2 = x1 + x2 + u1 + u2
Write the equations in standard matrixform and identify the A, B, C, and D matrices
Draw a simulation (block) diagram.

Use Row Reduction and Back Substitution to solve the given Linear System of Equations. Write the Augmented Matrix for each of them.
[Please refer to the attachment for the given linear system of equations].

Determine the solutions of the system of equations whose matrix row is equivalent to
1011
0131
0000
Give three examples of the solutions. Verify that the solutions satisfy the original system of equations.

1. a) Consider the problem of cubic polynomial interpolation
p(xi) = yi, I = 0,1,23
with deg(p) ≤ 3 and x0, x1, x2, x3 distinct. Convert the problem of finding p(x) to another problem involving the solution of a system of linear equations.
b) Express the system from (a) in the form Ax = b, i

How do I express the following inhomogeneous system of first-order differential equations for x(t) and y(t) in matrixform?
(see the attachment for the full question)
x = -2x - y + 12t + 12,
y = 2x - 5y - 5
How do I express the corresponding homogeneous system of differential equations, also in matrixform?
How do I fin

Please help me with the quetions below. Thank you.
Do all matrices have a determinant? Why or why not? Provide an example of a matrix that does not have a determinant.
Do all matrices have an inverse? Why or why not? Provide an example of a matrix that does not have an inverse.

1) Let A be a square matrix with determinant equal to 0. Prove that if X is a solution to the equation Ax=b then every solution to this equation must have the form x=X+xot where xo is a solution of Ax=0.
2) Find a basis for the solution space of the following system of equations.
x- 2x2+ x3 =-4
-2x +3x2 + x4=6
3x -

Details: From the following augmented matrix, first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these equations and their unknowns. Be creative. Do not use word problems that are in the assignments or course material.