Lesson Worksheet: Matrix Multiplication Mathematics
In this worksheet, we will practice identifying the conditions for matrix multiplication and evaluating the product of two matrices if possible.
Q11:
Consider the matrix product
What can you conclude about it?
- AFor a given matrix , there cannot be any matrix except the identity matrix for which .
- BFor a given matrix , there can be a matrix that is not the identity matrix for which .
- CFor a given matrix , there can be a matrix that is not the identity matrix for which .
- DFor a given matrix , there can be a matrix that is not the identity matrix for which .
Is it possible to find a matrix with the above property for every matrix ?
- ANo
- BYes
Q13:
Consider the matrices Find if possible.
- A
- B
- C
- D
Q19:
Is it possible to have a matrix and a matrix such that If so, give an example.
- AYes, ;
- BNo
- CYes, ;
Q20:
Suppose the matrix product makes sense. We also know that has 2 rows, has 3 columns, and has 4 entries. Is it possible to determine the possible sizes of these matrices? If so, what are the possible sizes of , , and ?
- AYes, , , ; , , ; , ,
- BYes, , , ; , , ; , ,
- CYes, , , ; , , ; , ,
- DNo
- EYes, , , ; , , ; , ,
Q21:
Find the matrices and such that, for any matrix , and . Explain why and are not the same.
- A, , and have different dimensions.
- B, , and have different dimensions.
- C, , and have different dimensions.
- D, , and have different dimensions.
- E, , and have different dimensions.
Q24:
Suppose is a matrix, is a matrix, and is a matrix. What are the sizes of the product matrices , and ?
- A
- B
- C
- D
- E
Q25:
If is a matrix of order and is a matrix of order , then what is the order of ?
- A
- B
- C
- D