Question
Download Solution PDFLet X be a matrix of order 3 x 3, Y be a matrix of order 2 x 3 and Z be a matrix of order 3 × 2. Which of the following statements are correct?
I. (ZY)X is defined and is a square matrix of order 3.
II. Y(XZ) is defined and is a square matrix of order 2.
III. X(YZ) is not defined.
Select the answer using the code given below.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Matrix Multiplication:
- Matrix multiplication is defined only when the number of columns in the first matrix is equal to the number of rows in the second matrix.
- For two matrices
and , their product will result in a matrix . - In general, the product of
and is defined if and only if the number of columns in equals the number of rows in .
Calculation:
We have the following matrix operations:
Now, consider the matrix multiplications:
Finally, we observe that:
Conclusion:
Hence, X(YZ) is not defined.
∴ the Correct answer is Option 4
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