MATH SOLVE

3 months ago

Q:
# The sizes of matrices A and B are given. Find the sizes of AB and BA whenever they are defined. (If the matrix product is undefined, enter UNDEFINED.)A is of size 6 × 7, and B is of size 7 × 6.AB ______x________BA _____x_________

Accepted Solution

A:

Answer: The required answers areAB is of order 6 × 6.
BA is of order 7 × 7.Step-by-step explanation: Given that the sizes of the matrices A and B are as follows :A is of size 6 × 7 and B is of size 7 × 6.We are to find the sizes of AB and BA whenever they are defined.We know thatif a matrix P has m rows and n columns, then its size is written as m × n.Also, two matrices P and Q of sizes m × n and r × s respectively can be multiplies if the number of columns in P is equal to the number of rows in Q.That is, if n = r. And the size of the matrix P × Q is m × s.Now, since the number of columns in A is equal to the number of rows in B, the product A × B is possible and is of order 6 × 6.Similarly, the number of columns in B is equal to the number of rows in A, the product B × A is possible and is of order 7 × 7.Thus, the required answers areAB is of order 6 × 6.
BA is of order 7 × 7.