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 .
Multone 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.
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 Description: elementary questions on matrices. serveur web interactif avec des cours en ligne, des exercices interactifs en sciences et langues pour l'enseigment primaire, secondaire et universitaire, des calculatrices et traceurs en ligne
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