8.3. Matrices to Represent Data http://www.ck12.org
Real photos and computer images have matrices that are much larger and include more numbers than just zero and
one to account for more colors.
Vocabulary
Amatrixis a rectangular array of numbers used to represent data in a compact and efficient way.
Asquare matrixis a matrix with the same number of rows and columns.
Anidentity matrixis a matrix with zeros everywhere except along the diagonal where there are ones.
Adiagonal matrixis a matrix with zeros everywhere except along the diagonal where the numbers can be anything.
Thetranspose of a matrixis a new matrix whose columns and rows have been switched. This changes the order of
the matrix from, for example, 3×2 to 2×3.
Atriangular matrixis described as either upper or lower triangular. That portion of the matrix is entirely
zeros. These kinds of matrices are easier to solve.
Asymmetric matrixis a square matrix with reflection symmetry across the main diagonal.
Guided Practice
- Geetha took the SAT three times. The first time she scored 460 on math and 540 on verbal. The second time she
scored 540 on math and 620 on verbal. The third time she scored 650 on math and 670 on verbal. Use a matrix to
represent Geetha’s scores. - Write out the 5×4 matrix whose entries areai j=i+jj.
- Create a 3×3 matrix for each of the following:
a. Diagonal Matrix
b. Lower Triangular
c. Symmetric
d. Identity
Answers: - Let the rows represent each sitting and the columns represent math and verbal.
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