Matrices and Transpose

Question

 

Question One

 

Question Two

 

Answer 1

Question one

a) The augmented matrix is

The bottom row of the matrices is zero.

The system is inconsistent. There is no solution.

Question two

The matrices are

a)To find transpose of matrix A,

Write the rows of A as the columns of A^T

Write the columns of A as the rows of A^T

b)

Matrix multiplication

• If the number of columns in the first matrix is equal to the number of rows in second matrix then the multiplication is possible.
• Multiply the elements of each row of the first matrix by the elements of each column in the second matrix.
• Add the products.

Now calculate AB

Number of columns in A = 2, number of rows in B = 3

In this case AB is not possible.

• AB^T

 

• BA^T

• B^TB