This topic connects linear algebra with geometry by using matrices to represent and manipulate linear transformations in two and three dimensions. Students explore how specific matrices encode geometric operations such as rotations, reflections, enlargements, stretches, and shears. The curriculum covers the composition of transformations through matrix multiplication, the geometric interpretation of the determinant as an area or volume scale factor, and the calculation of inverse matrices to reverse transformations. Advanced analysis includes identifying invariant points and invariant lines to fully characterize the geometric effect of a matrix.
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Essential terms to know
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