Matrices are used in the science of optics **to account for reflection and for refraction**. Matrices are also useful in electrical circuits and quantum mechanics and resistor conversion of electrical energy. Matrices are used to solve AC network equations in electric circuits.

The term matrix was introduced by the 19th-century English mathematician **James Sylvester**, but it was his friend the mathematician Arthur Cayley who developed the algebraic aspect of matrices in two papers in the 1850s.

The advantage of the decision-making matrix is that **it encourages self-reflection amongst the members of a design team to analyze each candidate with a minimized bias** (for team members can be biased towards certain designs, such as their own).

Engineers use matrices to model physical systems and perform accurate calculations needed for complex mechanics to work. **Electronics networks, airplane and spacecraft, and in chemical engineering** all require perfectly calibrated computations which are obtained from matrix transformations.

A decision matrix can **help you not only make complex decisions, but also prioritize tasks, solve problems and craft arguments to defend a decision you've already made**. It is an ideal decision-making tool if you are choosing among a few comparable solutions with multiple quantitative criteria.

Among the most common tools in electrical engineering and computer science are rectangular grids of numbers known as matrices. **The numbers in a matrix can represent data, and they can also represent mathematical equations**.

Matrices are used in the science of optics **to account for reflection and for refraction**. Matrices are also useful in electrical circuits and quantum mechanics and resistor conversion of electrical energy. Matrices are used to solve AC network equations in electric circuits.

In the multiple regression setting, **because of the potentially large number of predictors, it is more efficient** to use matrices to define the regression model and the subsequent analyses.

proportionality, In algebra, **equality between two ratios**. In the expression a/b = c/d, a and b are in the same proportion as c and d. A proportion is typically set up to solve a word problem in which one of its four quantities is unknown.

The value of root 4 is equal to exactly 2. But the roots could be positive or negative or we can say there are always two roots for any given number. Hence, root 4 is equal to **±2 or +2 and -2 (positive 2 and negative 2)**.

Square Root From 1 to 50.

Number | Square Root Value |
---|---|

2 | 1.414 |

3 | 1.732 |

4 | 2 |

5 | 2.236 |

The scientific method is **a standardized way of making observations, gathering data, forming theories, testing predictions, and interpreting results**. Does this mean all scientists follow this exact process? No. Some areas of science can be more easily tested than others.

If the value in the radicand is negative, the root is said to be an imaginary number. The imaginary number i is defined as **the square root of negative 1**. √−1=i.

Connotation is the use of a word to suggest a different association than its literal meaning, which is known as denotation. For example, **blue is a color, but it is also a word used to describe a feeling of sadness, as in: “She's feeling blue.”** Connotations can be either positive, negative, or neutral.

The concept of imaginary numbers was first introduced by mathematician **“Euler”**. He was the one who introduced i (read as 'iota') to represent √-1. He also defined i2 = -1.

Denotation means the literal definition of a word. To give an example, the denotation for blue is the color blue. For example: The girl was blue.**Look at these denotation sentence examples.**

- The boy was pushy.
- She was cold.
- It was too hard.
- The dog is a mutt.
- Trevor is a bull.
- The woman was frugal.
- He was bull-headed.

Generally speaking, **quantitative analysis involves looking at the hard data, the actual numbers.** **Qualitative analysis is less tangible.** **It concerns subjective characteristics and opinions – things that cannot be expressed as a number**.

measuring a quantity

The **AAA similarity test**: If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

A square root is written with **a radical symbol √** and the number or expression inside the radical symbol, below denoted a, is called the radicand.

The RATIO OF SIMILARITY between any two similar figures is **the ratio of any pair of corresponding sides**. Simply stated, once it is determined that two figures are similar, all of their pairs of corresponding sides have the same ratio.

**There are four similarity tests for triangles.**

- Angle Angle Angle (AAA) If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.
- Side Angle Side (SAS)
- Side Side Side (SSS)
- Right-angle Hypotenuse Side (RHS)

Dated : 21-Jul-2022

Category : Education