3.5 Perform Basic Matrix Operations

A Matrix Is a rectangular arrangement of elements in rows and columns. The elements in a matrix are called it’s entries.

For Example Matrix A has dimension 2 x 4 (we say 2 by 4) columns a 6 5 7 -2 5 y x columns rows A= Matrix A has dimension 2 x 4 (we say 2 by 4) 3 2 6 B= Matrix B is a column matrix with dimension 3 x 1 5 -2 x z C= Matrix C is a 1 x 4 row matrix

A square Matrix has the same number of rows and columns. A matrix whose entries are all zeros is called the Zero Matrix. Two matrices are equal if their dimensions are the same and the entries in corresponding positions are equal.

Are matrices C and D equal? Z 5 4 -3 A= Z 5 4 -3 B= Matrix A and matrix B are both 2 x 2 and have the same elements in the same corresponding entries, so they are equal. 3 4 7 -9 f z s -2 C= 2 1 D= Are matrices C and D equal? No, they have different number of columns and rows and different elements.

In Matrix algebra, a real number is often called a scalar In Matrix algebra, a real number is often called a scalar. To multiply a matrix by a scalar, you multiply each entry in the matrix by the scalar. This process is called scalar multipliciation. scalar 5 6 7 -2 2 10 12 14 -4 = Solve the following problem involving matrices: 2x+1 6y-4 5 2 = 2x+1=5 6y-4=2 +4 +4 -1 -1 6y = 6 2x = 4 6 6 2 2 y= 1 x= 2

We can do Matrix Arithmetic like ADDITION or Subtraction 2 3 -2 5 4 6 7 10 + = = 6 9 5 15 2+4 3+6 -2+7 5+10 6 8 7 2 4 10 - = = 4 -8 6-2 8-4 7-7 2-10 3 -2 4 1 2 1 0 2 3 + = 6 -4 8 2 1 0 2 3 + 7 -4 10 5 = Notice that matrices that are added or subtracted have the same dimensions.