Key Concepts & Glossary

Key Concepts

  • A matrix is a rectangular array of numbers. Entries are arranged in rows and columns.
  • The dimensions of a matrix refer to the number of rows and the number of columns. A
    3×23\times 2
    matrix has three rows and two columns.
  • We add and subtract matrices of equal dimensions by adding and subtracting corresponding entries of each matrix.
  • Scalar multiplication involves multiplying each entry in a matrix by a constant.
  • Scalar multiplication is often required before addition or subtraction can occur.
  • Multiplying matrices is possible when inner dimensions are the same—the number of columns in the first matrix must match the number of rows in the second.
  • The product of two matrices,
    AA
    and
    BB
    , is obtained by multiplying each entry in row 1 of
    AA
    by each entry in column 1 of
    BB
    ; then multiply each entry of row 1 of
    AA
    by each entry in columns 2 of
    B,B,\text{}
    and so on.
  • Many real-world problems can often be solved using matrices.
  • We can use a calculator to perform matrix operations after saving each matrix as a matrix variable.

Glossary

column
a set of numbers aligned vertically in a matrix
entry
an element, coefficient, or constant in a matrix
matrix
a rectangular array of numbers
row
a set of numbers aligned horizontally in a matrix
scalar multiple
an entry of a matrix that has been multiplied by a scalar

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