Transpose Of a Matrix Problems and Solving

Transpose Of a Matrix Problems and Solving. In this math tutorial tutorial, we will still be talking about matters relating to the matrix. Our discussion this time is related to the transpose matrix.

Matrix in mathematics is a collection of numbers, symbols or rectangular expressions arranged according to rows and columns. The numbers contained in a matrix are called elements or are also called members of a matrix.

Matrices are widely used to solve various mathematical problems such as in finding solutions to the problem of linear equations, linear transformations ie the general form of linear functions eg rotations in 3 dimensions. The matrix is ​​also like an ordinary variable, so the matrix can be manipulated for example multiplied, summed, subtracted, and decomposed. Using a matrix representation, calculations can be performed more structured.

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The sum and subtraction in the matrix can only be done if both matrices have the same size or type. Elements in a summed or subtracted matrix are elements that have the same position / position.

The definition of a transpose matrix is ​​when a matrix is ​​exchanged between the column dimension and its row. Another definition of a transpose matrix is ​​a matrix obtained by moving elements in a column into a row element and vice versa. Usually a transpose matrix is ​​symbolized by using the quotes (A ') or with the small letter T above (A^T).

Transpose of matrix

Understanding of the transpose matrix is ​​a matrix that exchanged between the dimensions of the column and its row.

Another definition of the transpose matrix is ​​a matrix obtained by moving elements in a column into a row element and vice versa.

Suppose: Given a matrix A as below:

A =

a b c

Then the tranpose matrix is:

A^T =

a b c

Characteristics - Matrix Transpose

Transpose matrix has several properties that become the basis in matrix calculation operation, that is:

• (A + B)^T = A^T + B^T
• (A^T)^T = A
• λ(A^T) = (λA^T), bila λ suatu scalar
• (AB)^T = B^T A^T

Exercise Matrix Transpose Problem

Problem No.1
Find the matrix transpose value of the following 2x2 matrix A:

A =

4 3 8 7

Discussion:

A =

4 3 8 7

A ^T=

4 8 3 7

Problem No.2 : Transpose matrix 2x2
Find the matrix transpose value of the following 2x2 berxed X matrix:

X =

2 5 3 4

Discussion:

X =

2 5 3 4

X ^T=

2 3 5 4

Problem No.3
Find the matrix transpose values ​​of the following 3x3 berxed matrix A:

A =

1 2 3 6 5 4 7 8 9

Discussion:

A =

1 2 3 6 5 4 7 8 9

A ^T=

1 6 7 2 5 8 3 4 9

Problem No.4
Known two matrix orders 2x2 as below:

A =

1 2 4 3

   B =

5 6 8 7

Determine (A + B)^T ?

Discussion :

A + B =

1 2 4 3

  +

5 6 8 7

A + B =

1 + 5 2 + 6 4 + 8 3 + 7

A + B =

6    8 12 10

Then the result (A + B)^T :

(A + B)^T =

6 12 8 10

Problem No.5
Known two matrix orders 2x2 as below:

A =

2 1 3 5

   B =

3 4 1 2

Determine (A + B)^T ?

Discussion :

first calculate A + B so obtained:

A + B =

2 1 3 5

  +

3 4 1 2

A + B =

2 + 3 1 + 4 3 + 1 5 + 2

A + B =

5   5 4  7

column 1 = 5 and 4, while
column 2 = 5 and 7
so to calculate the transpose matrix, change the columns to rows.
Then the result (A + B)^T :

(A + B)^T =

5 4 5 7

Conclusion:

The transpose matrix is ​​a matrix that experiences the exchange of elements from columns to rows or vice versa.

So this article about "Transpose Of a Matrix Problems and Solving" may be useful