# Quizz matrices --- Introduction ---

This module contains 17 training exercises on basic notions of matrices: multiplication, inverse, trace, rank. See Quizz determinant for similar exercises on the determinant. Students may use them as a training tool for a better memorization of the lesson, while teachers may put them into a work sheet with activated time limit, so that proficiency can be tested.

### Size of AB

Let be a matrix , a matrix .

Give the condition for to make sense.

In this case, has rows and columns.

### ABA

We have a matrix , such that the multiplication
makes sense.

What is the size of ? ×

What is the size of ? ×

### ABC

We have a matrix , such that the multiplication
makes sense.

What is the size of ? rows and columns.

### Invertibility and coefficients

Let be a matrix. Is the following statement true?
If , .

### Invertibility

. Is the following statement true?
If , then .
( is the × identity matrix.)

### Matrix operations

Consider two matrices
.
• Does make sense ?
• Does make sense ?
• Does make sense ?
• Does make sense ?
• Does make sense ?

### Multiplicability

. Is the following statement true?
If , then .

### Mult-one 4x4

What is the value of in the following multiplication of matrices?

### Partial multiplication 3x3

We have an equation of multiplication of matrices × as follows, where the question marks represent unknown coefficients.
There is only one determinable coefficient in the product matrix. It is .
Type c11 for for example.

### Partial multiplication 4x4

We have an equation of multiplication of matrices × as follows, where the question marks represent unknown coefficients.
There is only one determinable coefficient in the product matrix. It is .
Type c11 for for example.

### Algebraic properties

Let be three × matrices, and and two numbers. Among the following properties, which ones are ?

### Algebraic properties II

. Is the following property true?
( is the × identity matrix.)

### Properties of multiplication

×. Is the following statement true?
If , then .
( is the × identity matrix.)

### Trace 2x2

What is the trace of the matrix
?

### Trace 3x3

What is the trace of the matrix
?

### Trace 4x4

What is the trace of the matrix
?

### Triangular invertibility 3x3

Determine whether the following matrix is invertible, where is a real number.
Other exercises on:

This page is not in its usual appearance because WIMS is unable to recognize your web browser.
In order to access WIMS services, you need a browser supporting forms. In order to test the browser you are using, please type the word wims here: and press Enter''.

Please take note that WIMS pages are interactively generated; they are not ordinary HTML files. They must be used interactively ONLINE. It is useless for you to gather them through a robot program.

• Description: elementary questions on matrices. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games
• Keywords: wims, mathematics, mathematical, math, maths, interactive mathematics, interactive math, interactive maths, mathematic, online, calculator, graphing, exercise, exercice, puzzle, calculus, K-12, algebra, mathématique, interactive, interactive mathematics, interactive mathematical, interactive math, interactive maths, mathematical education, enseignement mathématique, mathematics teaching, teaching mathematics, algebra, geometry, calculus, function, curve, surface, graphing, virtual class, virtual classes, virtual classroom, virtual classrooms, interactive documents, interactive document, algebra, linear_algebra, mathematics, matrix, rank