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How to Express Matrices Into a Single Matrix

A matrix, in mathematics, is a rectangular array of expressions typically used to represent transformations of linear functions such as f(x) = 2x + 1. Matrices are arranged with rows and columns, and each expression within a matrix is called an element. Expressing matrices as a single matrix involves matrix arithmetic. If two matrices are the same size, meaning they have the same number of rows and columns, they can be added or subtracted to form a single matrix. Matrices can be multiplied if the number of columns in the first matrix equals the number of rows in the second.

Instructions

Matrix Addition
- 1
  Ensure that the matrices have the same dimensions, such as 2x2, which means the matrices consist of two rows and two columns.
- 2
  Set up an addition operation between each element in one matrix and its corresponding element in the other matrix. For example, to add a 2x2 matrix containing the elements 4 and 5 in its first row and 2 and 6 in its second row to another 2x2 matrix containing 7 and 5 in its first row and 9 and 2 in its second row, set the expression up like this: (4 + 7) and (5 + 5) in the first row of the resultant matrix and (2 + 9) and (6 + 2) in the second row.
- 3
  Add to obtain the new single matrix expression for the sum of a set of matrices. For example, for a matrix with (4 + 7) and (5 + 5) in the first row and (2 + 9) and (6 + 2) in the second row, the new matrix becomes: 11 and 10 in the first row and 11 and 8 in the second row.
Matrix Subtraction
- 4
  Ensure that the matrices have the same dimensions, such as 2x2, which means the matrices consist of two rows and two columns.
- 5
  Set up a subtraction operation between each element in one matrix and its corresponding element in the other matrix. For example, to subtract a 2x2 matrix containing the elements 4 and 5 in its first row and 2 and 6 in its second row from another 2x2 matrix containing 7 and 5 in its first row and 9 and 2 in its second row, set the expression up like this: (4 - 7) and (5 - 5) in the first row of the resultant matrix and (2 - 9) and (6 - 2) in the second row.
- 6
  Subtract to obtain the new single matrix expression for the difference of a set of matrices. For example, for a matrix with (4 - 7) and (5 - 5) in the first row and (2 - 9) and (6 - 2) in the second row, the new matrix becomes: -3 and 0 in the first row and -7 and 4 in the second row.
Matrix Multiplication
- 7
  Ensure that the matrices have the same dimensions, such as 2x2, which means the matrices consist of two rows and two columns.
- 8
  Set up the multiplication operation between each element in each row of one matrix to the elements in the corresponding column of the other matrix. For example, to multiply a 2x2 matrix containing the elements 4 and 5 in its first row and 2 and 6 in its second row to another 2x2 matrix containing 7 and 5 in its first row and 9 and 2 in its second row, set the expression up like this: (4 * 7) + (4 * 9) and (5 * 7) + (5 * 9) in the first row of the new, combined matrix and (2 * 9) + (2 * 2) and (6 * 9) + (6 * 2) in the second row.
- 9
  Multiply to obtain the new single matrix expression for the difference of a set of matrices. For example, for a matrix with (4 * 7) + (4 * 9) and (5 * 7) + (5 * 9) in the first row and (2 * 9) + (2 * 2) and (6 * 9) + (6 * 2) in the second row, the new matrix becomes: (28 + 36) and (35 + 45) in the first row and (18 + 4) and (54 + 12) in the second row. Adding finds: 64 and 80 in the first row and 22 and 66 in the second row.

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