Given the matrix A=[00103010−10] and suppose that we have the following row reduction to its PREF B A=[00103010−10]⇒[10−10030001]⇒[10−10010001]⇒[100010001] Write A and A−1 as product of elementary matrices.

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Given the matrix  A=[00103010−10]  and suppose that we have the following row reduction to its PREF B  A=[00103010−10]⇒[10−10030001]⇒[10−10010001]⇒[100010001]  Write A and A−1 as product of elementary matrices.

broliY · Accepted Answer

Given the matrix A=[00103010−10] Write A and A−1 as product of elementary matrices. Step 2 Take the matrix A and exchange the first and second rows. Let E1 be the elementary row matrix corresponding to the above row operation. E1=[001010100] Notice that E1A=[10−10030001] Step 3 Next, take the matrix [10−10030001] and divide the second row by the scalar 3. Let E2 be the elementary row matrix corresponding to the above row operation. E2=[1000130001] Notice that E2[10−10030001]=[10−10010001] Step 4 Next, take the matrix [10−10010001] and add 10 times the third row to the first row. Let E3 be the elementary row matrix corresponding to the above row operation. E3=[1010010001] Notice that E3[10−10010001]=[100010001]=I Step 5 Now, I=E3[10−10010001]=E3E2[10−10030001]=E3E2E1A and so A−1=E3E2E1 , that is A−1=[1010010001][10−100130001][001010100] Step 6 Also, A=E1−1E2−1E3−1 =

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Given the matrix A=begin{bmatrix}0 & 0&1 0 & 3&0 1&0 & -10 end{bmatrix} and suppose that we have the following row reduction to its PREF B A=begin{bma

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