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 two numbers. Among the following properties, which ones are ?

1.
2.
3.
4.


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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