first we find the row transformations that take S into identity matrix.then using this we find elementary matrices .then we write inverse as a product.
9. s: ['o] Write s' as the product of elementary matrices, that is, matrices from the...
Consider some elementary row operation. Show that the corresponding elementary matrix is obtained by applying this row operation to the identity matrix. How do we know what size of identity matrix to use?
Algebra of matrices. 3. (a) If A is a square matrix, what does it mean to say that B is an inverse of A (b) Define AT. Give a proof that if A has an inverse, then so does AT. (c) Let A be a 3 x 3 matrix that can be transformed into the identity matrix by perform ing the following three row operations in the given order: R2 x 3, Ri R3, R3+2R1 (i) Write down the elementary...
2. Write the product of a sequence of elementary matrices which equals the given non-singular matrix: [ 11 2 3 3. Given the matrix A = 01 - write the matrix of minors of A, the matrix of cofactors of A, the adjoint 12 2 2 matrix of A, and use the adjoint of A, to write the inverse of A. 4. Determine whether the set of vectors is linearly dependent or linearly independent. Justify your answer. 13
Prove that type 1 elementary matrix is a product of type 2 and 3 elementary matrices
Write the matrix A- Do no leave any blanks. If you need fewer than five elementary matrices, fill the remaining spaces with identity matrice You may want to adjust the width of your browser window so that all matrices fit on one line. as a product of elementary matrices. -3 1
In exercises 2 and 2a, find as sequence of elementary matrices that can be used to write the matrix in row-echelon form. 2. A1 -1 2a. A [5 6 1
Let A = [111] 1 2 3. Write A as the product of elementary matrices. (1 4 5
1 3 1. Find the inverse using elementary matrices A 2-3 Find a sequence of elementary matrices whose product is the given matrix. 2-H 4 3 Find an LU-factorization. 3 01 6 1 1 3. -3 1 3 1. Find the inverse using elementary matrices A 2-3 Find a sequence of elementary matrices whose product is the given matrix. 2-H 4 3 Find an LU-factorization. 3 01 6 1 1 3. -3 1
4) a) For the system of equations given, partially row reduce the coefficient matrix in the following careful way: X1 + 2yı - 2 = 5 4x+9y, - 32 = 8 (5x + 12yı - 324 = 1 Stage 1: just reduce the matrix first to an upper triangular form U and leave pivot entries as they are (don't multiple to change them to 1's). Reduce from left to right through the columns and from the pivot entry down within...
2-1 1 Write M1 0as a product of elementary matrices and find the inverse of M.