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Quizz matrices

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.

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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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