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Intro to Matrices

Intro to Matrices. What is a matrix?. A Matrix is just rectangular arrays of items A typical matrix is a rectangular array of numbers arranged in rows and columns. Sizing a matrix. By convention matrices are “sized” using the number of rows (m) by number of columns (n). “Special” Matrices.

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Intro to Matrices

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  1. Intro to Matrices

  2. What is a matrix? • A Matrix is just rectangular arrays of items • A typical matrix is a rectangular array of numbers arranged in rows and columns.

  3. Sizing a matrix • By convention matrices are “sized” using the number of rows (m) by number of columns (n).

  4. “Special” Matrices • Square matrix: a square matrix is an mxn matrix in which m = n. • Vector: a vector is an mxn matrix where either m OR n = 1 (but not both).

  5. “Special” Matrices • Scalar: a scalar is an mxn matrix where BOTH m and n = 1. • Zero matrix: an mxn matrix of zeros. • Identity Matrix: a square (mxm) matrix with 1s on the diagonal and zeros everywhere else.

  6. Transposing a Matrix • Matrix Transpose: is the mxn matrix obtained by interchanging the rows and columns of a matrix (converting it to an nxm matrix)

  7. Matrix Addition • Matrices can be added (or subtracted) as long as the 2 matrices are the same size • Simply add or subtract the corresponding components of each matrix.

  8. Scalar multipication • - Scalar multiplication works like the distributive property with algebraic expressions. • Given find 2A • =2A

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