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Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Problem#7: Given the matrices: 4 -2 1 6 9 -4 A= 6 8 -5 B = 7 5 3 7 9 10 -8 2 1 Write TensorFlow code to verify the following properties: a. Associative property A(B+C) = AB + AC [[-31 -13 -7] [173 147 -25] [117 57 112]], shape=(3, 3), dtype=int32) -4 C = 10 3 Both sides of the above equation will evaluate to the following matrix. Ctf.Tensor( b. Distributive property (AB)C = A(BC) -5 27 6 1 -98 Both sides of the above equation will evaluate to the following matrix. Ctf.Tensor( [[ 209 347 -136] [297 -111 308] [1207 562 250]], shape=(3, 3), dtype=int32) Please notice that the matrix multiplication operation defined in Problem#7 is 'Matrix Product' (not element wise matrix multiplication). The matrix multiplication function in TensorFlow library is 'matmul'. Element wise matrix multiplication In mathematics, the Hadamard product is a binary operation that takes two matrices of the same dimensions and produces another matrix of the same dimension as the operands where each element i, j is the product of elements i, j of the original two matrices. It should not be confused with the more common matrix product. Matrix Product In mathematics, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The result matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix.
Transcribed Image Text:Problem#7: Given the matrices: 4 -2 1 6 9 -4 A= 6 8 -5 B = 7 5 3 7 9 10 -8 2 1 Write TensorFlow code to verify the following properties: a. Associative property A(B+C) = AB + AC [[-31 -13 -7] [173 147 -25] [117 57 112]], shape=(3, 3), dtype=int32) -4 C = 10 3 Both sides of the above equation will evaluate to the following matrix. Ctf.Tensor( b. Distributive property (AB)C = A(BC) -5 27 6 1 -98 Both sides of the above equation will evaluate to the following matrix. Ctf.Tensor( [[ 209 347 -136] [297 -111 308] [1207 562 250]], shape=(3, 3), dtype=int32) Please notice that the matrix multiplication operation defined in Problem#7 is 'Matrix Product' (not element wise matrix multiplication). The matrix multiplication function in TensorFlow library is 'matmul'. Element wise matrix multiplication In mathematics, the Hadamard product is a binary operation that takes two matrices of the same dimensions and produces another matrix of the same dimension as the operands where each element i, j is the product of elements i, j of the original two matrices. It should not be confused with the more common matrix product. Matrix Product In mathematics, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The result matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix.
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Problem#7: Given the matrices: 4 -2 1 6 9 -4 A= 6 8 -5 B = 7 5 3 7 9 10 -8 2 1 Write TensorFlow code to verify the following properties: a. Associative property A(B+C) = AB + AC [[-31 -13 -7] [173 147 -25] [117 57 112]], shape=(3, 3), dtype=int32) -4 C = 10 3 Both sides of the above equation will evaluate to the following matrix. Ctf.Tensor( b. Distributive property (AB)C = A(BC) -5 27 6 1 -98 Both sides of the above equation will evaluate to the following matrix. Ctf.Tensor( [[ 209 347 -136] [297 -111 308] [1207 562 250]], shape=(3, 3), dtype=int32) Please notice that the matrix multiplication operation defined in Problem#7 is 'Matrix Product' (not element wise matrix multiplication). The matrix multiplication function in TensorFlow library is 'matmul'. Element wise matrix multiplication In mathematics, the Hadamard product is a binary operation that takes two matrices of the same dimensions and produces another matrix of the same dimension as the operands where each element i, j is the product of elements i, j of the original two matrices. It should not be confused with the more common matrix product. Matrix Product In mathematics, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The result matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix.
Transcribed Image Text:Problem#7: Given the matrices: 4 -2 1 6 9 -4 A= 6 8 -5 B = 7 5 3 7 9 10 -8 2 1 Write TensorFlow code to verify the following properties: a. Associative property A(B+C) = AB + AC [[-31 -13 -7] [173 147 -25] [117 57 112]], shape=(3, 3), dtype=int32) -4 C = 10 3 Both sides of the above equation will evaluate to the following matrix. Ctf.Tensor( b. Distributive property (AB)C = A(BC) -5 27 6 1 -98 Both sides of the above equation will evaluate to the following matrix. Ctf.Tensor( [[ 209 347 -136] [297 -111 308] [1207 562 250]], shape=(3, 3), dtype=int32) Please notice that the matrix multiplication operation defined in Problem#7 is 'Matrix Product' (not element wise matrix multiplication). The matrix multiplication function in TensorFlow library is 'matmul'. Element wise matrix multiplication In mathematics, the Hadamard product is a binary operation that takes two matrices of the same dimensions and produces another matrix of the same dimension as the operands where each element i, j is the product of elements i, j of the original two matrices. It should not be confused with the more common matrix product. Matrix Product In mathematics, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The result matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix.
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