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Problem P6.5. Consider the matrix $A = \begin{bmatrix} 2 & -1 \\ 1 & 3 \end{bmatrix}$. (a) Find an elementary matrix decomposition of A. Do this by hand and show how you get each elementary matrix. (b) Use your elementary matrix decomposition to describe in complete sentences, using geometric words, how A transforms the plane. (c) Use your decomposition to clearly sketch and label each step of how A transforms the plane. Do so by following the standard unit square. You may do this either carefully by hand or on GeoGebra. (d) Exploration. Is the elementary matrix decomposition you found unique? In other words, could you have found a different collection of elementary matrices whose product is A? Explain.

          Problem P6.5. Consider the matrix $A = \begin{bmatrix} 2 & -1 \\ 1 & 3 \end{bmatrix}$.
(a) Find an elementary matrix decomposition of A. Do this by hand and show how you get each elementary matrix.
(b) Use your elementary matrix decomposition to describe in complete sentences, using geometric words, how A transforms the plane.
(c) Use your decomposition to clearly sketch and label each step of how A transforms the plane. Do so by following the standard unit square. You may do this either carefully by hand or on GeoGebra.
(d) Exploration. Is the elementary matrix decomposition you found unique? In other words, could you have found a different collection of elementary matrices whose product is A? Explain.

Problem P6.5. Consider the matrix A =
< b m a t r i x >.
(a) Find an elementary matrix decomposition of A. Do this by hand and show how you get each elementary matrix.
(b) Use your elementary matrix decomposition to describe in complete sentences, using geometric words, how A transforms the plane.
(c) Use your decomposition to clearly sketch and label each step of how A transforms the plane. Do so by following the standard unit square. You may do this either carefully by hand or on GeoGebra.
(d) Exploration. Is the elementary matrix decomposition you found unique? In other words, could you have found a different collection of elementary matrices whose product is A? Explain.

Added by Gregorio S.

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