Question

ذرا 3 (2 points) Write X = as a product 0 X = E1 E2 E3 of elementary matrices. x= d] Ei E = E2 = E3 = =

Answer 1

To express X as a product of elementary matrices, perform row operations on an identity matrix until it becomes equal to X.

Step-by-step explanation:

To express X as a product of elementary matrices, we need to perform row operations on an identity matrix until it becomes equal to X. Each row operation can be represented by an elementary matrix. Let's go step by step:

Step 1: Start with the identity matrix, I.
Step 2: Apply the row operation that transforms I into X. Let's say this elementary matrix is E1.
Step 3: Repeat step 2 if necessary, applying a new elementary matrix each time. Let's say the next elementary matrix is E2.
Step 4: Continue until X is obtained by performing row operations using elementary matrices E1, E2, E3, and so on.

So, the product of elementary matrices representing X would be E = E1 * E2 * E3 * ...

Answer 2

To write X as a product of elementary matrices, perform the elementary row operations needed to transform the matrix X into row echelon form and record the resulting matrices at each step.

Step-by-step explanation:

To write X as a product of elementary matrices, we need to express X as a sequence of elementary row operations. Each elementary row operation can be represented by an elementary matrix.

Let E1, E2, and E3 represent the elementary matrices corresponding to the elementary row operations needed to transform the matrix X into its row echelon form. Then, X can be expressed as a product of E1, E2, and E3: X = E1 * E2 * E3.

To find the values of E1, E2, and E3, you would need to perform the elementary row operations on the matrix X and record the resulting matrices at each step.