Example of Multiplication Inverse Matrix and its Discussion

Formula.co.id – After previously we discussed about Examples of Logarithmic Problems this time we will discuss material about examples of complete matrix questions with discussion, we will describe in detail and completely from the meaning of the matrix, the types, formulas and examples of questions along with the discussion.

Definition of Matrix

Matrix is a collection of numbers that can be arranged in rows or columns or can also be arranged with both and enclosed in brackets. The elements of the matrix consist of certain numbers that form in a matrix.

This matrix itself is used to simplify the delivery of data, so that it will be easier to process further.

Matrices like ordinary variables can be manipulated, such as multiplied, added, subtracted and decomposed. With matrix representation, calculations can be done in a more structured manner.

Kinds of Matrix

There are various types of matrices, including:

1. Row Matrix

Row Matrix is ​​a matrix that consists of only one row.

Example:

P = [3 2 1]

Q = [4 5 – 2 5]

2. Column Matrix

Column Matrix is ​​a matrix that consists of only one column.

Example:

3. Square Matrix

Square Matrix is ​​a matrix where the number of rows is equal to the number of columns. If the number of rows of a square matrix A is n then the number of columns is also n, so the order of matrix A is n × n. Often a matrix A of order n × n can be called a square matrix of order n. The elements a11, a22, a33, …, ann are the elements on the main diagonal.

Example:

The main diagonal elements of matrix A are = 1 and 10, while in matrix B are = 4, 6, 13, and 2.

4. Diagonal Matrix

The Diagonal Matrix is ​​a square matrix with every element that is not a diagonal element whose main diagonal is 0 (zero), while the elements on the main diagonal are not all zero.

Example:

5. Identity Matrix

Identity Matrix is ​​a square matrix with all elements on the main diagonal are 1 (one) and all other elements are 0 (zero). In general, the identity matrix can be denoted by I and accompanied by its order.

Example:

6. Zero Matrix

Zero Matrix, which is a matrix in which all elements are 0 (zero). The zero matrix is ​​usually denoted by the letter O followed by its order, O_{m x n.}

Example:

Example of Matrix Questions and their Discussion

Below is an example of a question inverse matrix, multiplication matrices, and transpose, addition, and subtraction matrices along with their discussion and answers…

1. It is known that A = , B = , C = , Define:

• A + B :
• A + C :

Solution:

• A + B = =
• A + C = cannot be added because the order is not the same.

2. If A = and B = is =….

Solution:

• B – A = –
• B – A = =

The properties of addition and subtraction of a matrix are:

• A + B = B + A
• (A + B) + C = A + (B + C)
• A – B B – A

3. If matrix and mutually inverse, determine the value of x !

Solution:

It is known that the two matrices above are mutually inverse, then the condition AA syarat applies^-1 = A^-1A = I.

Then:

So that the 1st row element in the 1st column has the following equation:

• 9(x -1) – 7x = 1
• 9x – 9 – 7x = 1
• 2x = 10
• x = 5

So, the value of x is = 5

4. It is known that A = , Determine the value of 3A !

Solution:

• 3A = 3
• 3A =

So, the value of 3A is =

5. Determine the following values ​​for x, y, and z, if:

Solution:

Then:
z = 1 ………………………………….……..(1)
–2y – 4x = –10
y + 2x = 5

y = 5 – 2x ..………………………………. (2)
6y + 2x = 3x + 4
6y + 2x – 3x = 4

6y – x = 4 …………………………… (3)

(2) will be substituted into (3), so that it becomes:

6(5 – 2x) – x = 4
30 – 12x – x = 4
–13x = –26 then x = 2
y = 5 – 2(2) = 1
z = 1

This is a complete discussion of matrices along with formulas and examples of questions and their discussion, hopefully it will be useful…

Also Read:

• Matrix Multiplication
• Absolute Value Inequality