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Let A, B, C, and D be four matrices of dimensions 10 x 9, 9 x 12, 12 x 10, and 10 x 15, respectively. The minimum number of scalar multiplications required to find the product ABCD using the basic matrix multiplication method is ______.
Correct answer is '3480'. Can you explain this answer?
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Verified Answer
Let A, B, C, and D be four matrices of dimensions 10 x 9, 9 x 12, 12 x...
((AB)C)D = (10 x 9, 9 x 12), 12 x 10, 10 x 15
= 10 x 9 x 12 + 10 x 12 x 10 + 10 x 10 x 15
= 3780
A(BC)D =9 x 12 x 10 + 10 x 9 x 10 + 10 x 10 x 15
= 3480
A(B(CD)) = 12 x 10 x 15 + 9 x 12 x 15 + 10 x 9 x 15
= 4770
(AB)(CD) = 10 x 9 x 12 + 12 x 10 x 15 + 10 x 12 x 15
= 4680
Most Upvoted Answer
Let A, B, C, and D be four matrices of dimensions 10 x 9, 9 x 12, 12 x...
Solution:
Basic matrix multiplication method is also known as the naive method, which is used to find the product of two matrices. In this method, we multiply each element of a row of the first matrix with each element of a column of the second matrix and add them to get the corresponding element of the resulting matrix. This process is repeated for all the rows and columns of the matrices.
To find the product of ABCD using the basic matrix multiplication method, we need to follow the following steps:
Step 1: Multiply matrices A and B to get a matrix of dimension 10 x 12.
- Number of scalar multiplications required = (10 x 9 x 12) = 1080
Step 2: Multiply matrix C with the matrix obtained in step 1 to get a matrix of dimension 10 x 10.
- Number of scalar multiplications required = (10 x 12 x 10) = 1200
Step 3: Multiply matrix D with the matrix obtained in step 2 to get a matrix of dimension 10 x 15.
- Number of scalar multiplications required = (10 x 10 x 15) = 1500
Therefore, the minimum number of scalar multiplications required to find the product ABCD using the basic matrix multiplication method is:
Total number of scalar multiplications = 1080 + 1200 + 1500 = 3480
Hence, the correct answer is 3480.
Basic matrix multiplication method is also known as the naive method, which is used to find the product of two matrices. In this method, we multiply each element of a row of the first matrix with each element of a column of the second matrix and add them to get the corresponding element of the resulting matrix. This process is repeated for all the rows and columns of the matrices.
To find the product of ABCD using the basic matrix multiplication method, we need to follow the following steps:
Step 1: Multiply matrices A and B to get a matrix of dimension 10 x 12.
- Number of scalar multiplications required = (10 x 9 x 12) = 1080
Step 2: Multiply matrix C with the matrix obtained in step 1 to get a matrix of dimension 10 x 10.
- Number of scalar multiplications required = (10 x 12 x 10) = 1200
Step 3: Multiply matrix D with the matrix obtained in step 2 to get a matrix of dimension 10 x 15.
- Number of scalar multiplications required = (10 x 10 x 15) = 1500
Therefore, the minimum number of scalar multiplications required to find the product ABCD using the basic matrix multiplication method is:
Total number of scalar multiplications = 1080 + 1200 + 1500 = 3480
Hence, the correct answer is 3480.
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Let A, B, C, and D be four matrices of dimensions 10 x 9, 9 x 12, 12 x 10, and 10 x 15, respectively. The minimum number of scalar multiplications required to find the product ABCD using the basic matrix multiplication method is ______.Correct answer is '3480'. Can you explain this answer?
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