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
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:
matrices
determinant
linear algebra
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