Size of AB
Let
be a matrix $val18,
a matrix $val19. 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 $val24 matrix. Is the following statement true? If $val21, $val22.
Invertibility
$val25. Is the following statement true? If $val20, then $val21.
(
is the $val18×$val18 identity matrix.)
Matrix operations
Consider two matrices
.
Does
make sense? |
|
Does
make sense? |
|
Does
make sense? |
|
Does
make sense? |
|
Does
make sense? |
|
Multiplicability
$val19$val17. Is the following statement true? If $val14, then $val15.
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 $val6×$val6 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 $val6×$val6 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 $val6×$val6 matrices, and
two numbers. Among the following properties, which ones are $val23? 1.$val22 |
|
2.$val22 |
|
3.$val22 |
|
4.$val22 |
|
Algebraic properties II
$val28. Is the following property true? $val26
(
is the $val22×$val22 identity matrix.)
Properties of multiplication
$val21 $val15×$val15. Is the following statement true? If $val17, then $val18.
(
is the $val15×$val15 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.