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Intro to matrices

Matrix is an arrangement of numbers into rows and columns. Make your first introduction with matrices and learn about their dimensions and elements.
A matrix is a rectangular arrangement of numbers into rows and columns.
For example, matrix A has two rows and three columns.

Matrix dimensions

The dimensions of a matrix tells its size: the number of rows and columns of the matrix, in that order.
Since matrix A has two rows and three columns, we write its dimensions as 2×3, pronounced "two by three".
In contrast, matrix B has three rows and two columns, so it is a 3×2 matrix.
B=[8423121810]
When working with matrix dimensions, remember rows×columns!

Check your understanding

1) What are the dimensions of matrix D?
D=[724    2115  11912   0831]
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
×
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

2) What are the dimensions of matrix E?
E=[261308310]
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
×
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

3) What are the dimensions of matrix F?
F=[2010]
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
×
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Matrix elements

A matrix element is simply a matrix entry. Each element in a matrix is identified by naming the row and column in which it appears.
For example, consider matrix G:
G=[41471851320422]
The element g2,1 is the entry in the second row and the first column.
In this case g2,1=18.
In general, the element in row i and column j of matrix A is denoted as ai,j.

Check your understanding

4) A=[24   815526   2]
a1,3=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

5) B=[122.34.61.2]
b2,1=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

6) Matrix C is a 2×3 matrix with c1,2=6.
Which could be matrix C?
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