Answered Essay: For each part, you should provide your query and sample input and output from a mysql run. a) W

For each part, you should provide your query and sample input and output from a mysql run. Write a SQL query that will add two 2-dimensional matrices of arbitrary but equal size, A and B. a) b) Write a SQL query that will multiply a matrix A by a scalar, s. Do not use an SFW query and it should be independent of the matrix dimensions. c) Write a SQL query to multiply two matrices together. The first matrix A must have the same number of rows as the second matrix B has columns. Matrix multiplication is defined as Clij) =A(i,k) * B(hj)

For each part, you should provide your query and sample input and output from a mysql run. a) Write a SQL query that will add two 2-dimensional matrices of arbitrary but equal size, A and B. b) Write a SQL query that will multiply a matrix A by a scalar, s. Do not use an SFW query and it should be independent of the matrix dimensions. c) Write a SQL query to multiply two matrices together. The first matrix A must have the same number of rows as the second matrix B has columns. Matrix multiplication is defined as C(i, j) = A(i, k) * B(k, j).

Expert Answer

 

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/*Solution (a)*/
/*Create table for matrix A*/
CREATE TABLE AMatrix (rowNo INT, colNo INT, value INT, PRIMARY KEY(rowNo, colNo));
/*Create table for matrix B*/
CREATE TABLE BMatrix (rowNo INT, colNo INT, value INT, PRIMARY KEY(rowNo, colNo));
/*Insert values for matrix A*/
INSERT INTO AMatrix (rowNo, colNo, value) VALUES
(1, 1, 2),
(1, 2, 2),
(1, 3, 2),
(2, 1, 2),
(2, 2, 2),
(2, 3, 2);
/*Insert values for matrix B*/
INSERT INTO BMatrix (rowNo, colNo, value) VALUES
(1, 1, 2),
(1, 2, 2),
(1, 3, 2),
(2, 1, 2),
(2, 2, 2),
(2, 3, 2);
/*Query for matrix addition*/
SELECT A.rowNo, A.colNo, (A.value + B.value) AS value
FROM AMatrix AS A, BMatrix AS B
WHERE A.rowNo = B.rowNo
AND A.colNo = B.colNo;

/*Solution (b)*/
/*Create table for matrix A*/
CREATE TABLE AMatrix (rowNo INT, colNo INT, value INT, PRIMARY KEY(rowNo, colNo));
/*Create table for matrix B*/
CREATE TABLE BMatrix (rowNo INT,colNo INT,value INT, PRIMARY KEY(rowNo, colNo));
/*Insert values for matrix A*/
INSERT INTO AMatrix (rowNo, colNo, value) VALUES
(1, 1, 2),
(1, 2, 2),
(1, 3, 2),
(2, 1, 2),
(2, 2, 2),
(2, 3, 2);
/*Insert values for matrix B*/
INSERT INTO BMatrix (rowNo, colNo, value) VALUES
(1, 1, 2),
(1, 2, 2),
(1, 3, 2),
(2, 1, 2),
(2, 2, 2),
(2, 3, 2);
/*Query for matrix scalar multiplication*/
SELECT A.rowNo, B.colNo, SUM(A.value * 10) AS value
FROM AMatrix A
INNER JOIN BMatrix B
ON A.colNo = B.rowNo
GROUP BY A.rowNo, B.colNo;

/*Solution (c)*/
/*Create table for matrix A*/
CREATE TABLE AMatrix (rowNo INT, colNo INT, value INT, PRIMARY KEY(rowNo, colNo));
/*Create table for matrix B*/
CREATE TABLE BMatrix (rowNo INT,colNo INT,value INT, PRIMARY KEY(rowNo, colNo));
/*Insert values for matrix A*/
INSERT INTO AMatrix (rowNo, colNo, value) VALUES
(1, 1, 2),
(1, 2, 2),
(1, 3, 2),
(2, 1, 2),
(2, 2, 2),
(2, 3, 2);
/*Insert values for matrix B*/
INSERT INTO BMatrix (rowNo, colNo, value) VALUES
(1, 1, 2),
(1, 2, 2),
(1, 3, 2),
(2, 1, 2),
(2, 2, 2),
(2, 3, 2);
/*Query for matrix multiplication*/
SELECT A.rowNo, B.colNo, SUM(A.value * B.value) AS value
FROM AMatrix A
INNER JOIN BMatrix B
ON A.colNo = B.rowNo
GROUP BY A.rowNo, B.colNo;

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