Matrix Multiplication :
Matrix Multiplication How to multiply two matrices Slide 2:
Matrix multiplication falls into two general categories: Scalar in which a single number is multiplied with every entry of a matrix
Multiplication of an entire matrix by another entire matrix For the rest of the page, matrix multiplication will refer to this second category. Scalar Matrix Multiplication :
Scalar Matrix Multiplication In the scalar variety, every entry is multiplied by a number, called a scalar. Slide 4:
What is the answer to the scalar multiplication problem below? Solution: Matrix Multiplication :
Matrix Multiplication You can multiply two matrices if, and only if, the number of columns in the first matrix equals the number of rows in the second matrix. Otherwise, the product of two matrices is undefined. The product matrix's dimensions are (rows of first matrix) × (columns of the second matrix ) Slide 6:
In the picture on the left, the matrices can be multiplied since the number of columns in the 1st one, matrix A, equals the number of rows in the 2nd, matrix B. The Dimensions of the product matrix
Rows of 1st matrix × Columns of 2nd
4 × 3 Generalized ExampleIf we multiply a 2×3 matrix with a 3×1 matrix, the product matrix is 2×1 :
Generalized ExampleIf we multiply a 2×3 matrix with a 3×1 matrix, the product matrix is 2×1 Here is how we get M11 and M22 in the product.
M11 = r11× t11 + r12× t21 + r13×t31 M12 = r21× t11 + r22× t21 + r23×t31 Slide 8:
Matrix C and D below cannot be multiplied together because the number of columns in C does not equal the number of rows in D. In this case, the multiplication of these two matrices is not defined. How To Multiply Matrices :
How To Multiply Matrices In order to multiply matrices,
Step 1: Make sure that the the number of columns in the 1st one equals the number of rows in the 2nd one. (The pre-requisite to be able to multiply)
Step 2: Multiply the elements of each row of the first matrix by the elements of each column in the second matrix.
Step 3: Add the products. Is the product of matrix A and Matrix B below defined ? :
Is the product of matrix A and Matrix B below defined ? Since the number of columns in Matrix A does not equal the number of rows in Matrix B. The multiplication of A and B is undefined. :
Since the number of columns in Matrix A does not equal the number of rows in Matrix B. The multiplication of A and B is undefined. Slide 12:
Lets try this one … Slide 13:
Keep practicing……….