 13.1 Matrices and Their Sums

Presentation on theme: "13.1 Matrices and Their Sums"— Presentation transcript:

13.1 Matrices and Their Sums

A is a rectangular arrangement of numbers in rows and columns.
Matrix A below has two rows and three columns. The of matrix A are 2X3 (two by three; rows then columns). The numbers in the matrix are called matrix dimensions elements 2 rows 3 columns

Types of Matrices Name Description Example Row Matrix has only one row
Column Matrix Square Matrix has only one row has only one column has same number of rows as number of columns (i.e. 2X2)

For two matrices of the same dimensions, the entries in the same row and same column are said to be entries. Two matrices are if and only if they have the same dimensions and all of their corresponding entries are equal. corresponding equal

Find the value of the variables for which the given statement is true.
1.

Find the value of the variables for which the given statement is true.
2.

If two matrices A and B have the
If two matrices A and B have the dimensions, then their sum, A + B, is the matrix of the same dimensions whose entries are the sums of the entries of A and B. same corresponding

Find the sum. 3.

Find the sum. 4.

Zero Matrix Zero Matrix: Also called the identity matrix for addition

Opposite Matrix Note: , so –A is the additive of A.
Opposite Matrix: Changes the sign of each element in the matrix Note: , so –A is the additive of A. When subtracting two matrices, we the of the subtracted matrix. inverse add opposite

Find the difference. 5.

Find the difference. 6.

Find the value of the variables for which the given statement is true.
7.