Are Form 8854 Reduction 2023-2024

Hi, welcome to recitation. My name is Martina and I'll be a recitation instructor for some of these linear algebra videos. Today's problem is a straightforward one: solve the following linear system with four equations and four unknowns using the method of elimination. The system is: X - y - Z + U = 2 X + 2Z = 8 -y - 2Z = -8 3X - 3y - 2Z + 4U = 7 Although there are different ways to solve this system, we will use the method of elimination, which will be discussed extensively in these videos. It is important to learn and understand this method correctly. I suggest you try solving this system now using the method of elimination as described in class. Pause the video, solve it yourself, and then come back to compare your solution with mine. Now, let's proceed with the method of elimination. This method involves replacing the system with an equivalent system through a series of row operations. Row operations include exchanging the order of two equations, multiplying an equation with a non-zero number, and adding a non-zero multiple of one equation to another. To make it easier, we will represent the system in matrix form. Each row of the matrix corresponds to an equation, and each column corresponds to an unknown. Let's write the matrix: [1 -1 -1 1; 2 0 2 0; -1 -2 0 0; 3 -3 -2 4] Now, let's add the right-hand side of the equations to this augmented matrix: [1 -1 -1 1 8; 2 0 2 0 -8; -1 -2 0 0 7] To solve the system, we want to transform this matrix into an upper triangular matrix. We start with the first column and use the pivot (the number in the first row) to eliminate the numbers below it by ing row operations. In this case, we can...