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Algebra (all content)

Course: Algebra (all content) > Unit 20

Lesson 1: Introduction to matrices
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Algebra (all content)
Matrices
Introduction to matrices
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Intro to matrices

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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 start color #11accd, start text, t, w, o, space, r, o, w, s, end text, end color #11accd and start color #e07d10, start text, t, h, r, e, e, space, c, o, l, u, m, n, s, end text, end color #e07d10, we write its dimensions as start color #11accd, 2, end color #11accd, times, start color #e07d10, 3, end color #e07d10, pronounced "two by three".
In contrast, matrix B has start color #11accd, start text, t, h, r, e, e, space, r, o, w, s, end text, end color #11accd and start color #e07d10, start text, t, w, o, space, c, o, l, u, m, n, s, end text, end color #e07d10, so it is a start color #11accd, 3, end color #11accd, times, start color #e07d10, 2, end color #e07d10 matrix.
B=[−8−423121810]B=\left[\begin{array}{rr}-8 & -4 \\ 23 & 12 \\18 &10 \end{array}\right]
When working with matrix dimensions, remember start color #11accd, start text, r, o, w, s, end text, end color #11accd, times, start color #e07d10, start text, c, o, l, u, m, n, s, end text, end color #e07d10!

Check your understanding

1) What are the dimensions of matrix D?
D=[−724    2115  11−912   08−3−1]D=\left[\begin{array}{rr}-7 & 24 &~~~~2 \\ 1 & 15 &~~11 \\-9 &12&~~~0 \\8 &-3&-1 \end{array}\right]
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
times
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

2) What are the dimensions of matrix E?
E=[−26130−8310]E=\left[\begin{array}{rr}-2 & 6 &1 &3 \\ 0& -8 &3&10 \end{array}\right]
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
times
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

3) What are the dimensions of matrix F?
F=[−2010]F=\left[\begin{array}{rr}-2 \\ 0& \\10 \end{array}\right]
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
times
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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=[414−718513−20422]G=\left[\begin{array}{rr}4& 14&-7 \\ 18 & 5&13 \\-20 &4&22 \end{array}\right]
The element g, start subscript, start color #11accd, 2, end color #11accd, comma, start color #e07d10, 1, end color #e07d10, end subscript is the entry in the start color #11accd, start text, s, e, c, o, n, d, space, r, o, w, end text, end color #11accd and the start color #e07d10, start text, f, i, r, s, t, space, c, o, l, u, m, n, end text, end color #e07d10.
In this case g, start subscript, 2, comma, 1, end subscript, equals, start color #ca337c, 18, end color #ca337c.
In general, the element in start color #11accd, start text, r, o, w, space, end text, i, end color #11accd and start color #e07d10, start text, c, o, l, u, m, n, space, end text, j, end color #e07d10 of matrix A is denoted as a, start subscript, start color #11accd, i, end color #11accd, comma, start color #e07d10, j, end color #e07d10, end subscript.

Check your understanding

4) A=[2−4   815−5−26   2]A=\left[\begin{array}{rr}2 & -4 &~~~8 \\ 1 & 5&-5 \\-2 &6&~~~2 \end{array}\right]
a, start subscript, 1, comma, 3, end subscript, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

5) B=[12−2.34.61.2]B=\left[\begin{array}{rr}12 & -2.3 \\ 4.6 & 1.2& \end{array}\right]
b, start subscript, 2, comma, 1, end subscript, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

6) Matrix C is a 2, times, 3 matrix with c, start subscript, 1, comma, 2, end subscript, equals, 6.
Which could be matrix C?
Choose 1 answer:

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