2 2.9 © 2016 Pearson Education, Inc. Matrix Algebra DIMENSION AND RANK.

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2 2.9 © 2016 Pearson Education, Inc. Matrix Algebra DIMENSION AND RANK

Slide © 2016 Pearson Education, Inc. COORDINATE SYSTEMS

Slide © 2016 Pearson Education, Inc. COORDINATE SYSTEMS

Slide © 2016 Pearson Education, Inc. COORDINATE SYSTEMS

Slide © 2016 Pearson Education, Inc. COORDINATE SYSTEMS

Slide © 2016 Pearson Education, Inc. COORDINATE SYSTEMS

Slide © 2016 Pearson Education, Inc. THE DIMESION OF A SUBSPACE  Definition: The dimension of a nonzero subspace H, denoted by dim H, is the number of vectors in any basis for H. The dimension of the zero subspace {0} is defined to be zero.  Definition: The rank of a matrix A, denoted by rank A, is the dimension of the column space of A.

Slide © 2016 Pearson Education, Inc. THE DIMESION OF A SUBSPACE

Slide © 2016 Pearson Education, Inc. THE DIMESION OF A SUBSPACE

Slide © 2016 Pearson Education, Inc. RANK AND THE INVERTIBLE MATRIX THEOREM

Slide © 2016 Pearson Education, Inc. RANK AND THE INVERTIBLE MATRIX THEOREM

Slide © 2016 Pearson Education, Inc. RANK AND THE INVERTIBLE MATRIX THEOREM