All Linear Algebra Resources
Example Questions
Example Question #32 : Matrices
If is a
matrix and
is a
matrix, can the product
be multiplied? What about
?
can be multiplied
cannot be multiplied
can be multiplied
can be multiplied
cannot be multiplied
cannot be multiplied
cannot be multiplied
can be multiplied
can be multiplied
cannot be multiplied
If is an
matrix and
is an
matrix,
can only be multiplied if
.
Since is a
matrix and
is a
matrix,
and
can be multiplied.
has
rows and
has
columns, therefore
cannot be multiplied.
Example Question #32 : Matrices
If is a
matrix and
is a
matrix, what are the dimensions of the product
?
cannot be multiplied
If is an
matrix and
is an
matrix, the dimensions of
are
.
In this problem, If is a
matrix and
is a
matrix, so
the dimensions of are
.
Example Question #31 : Matrices
If is a
matrix and
is a
matrix, what are the dimensions of the product
?
cannot be multiplied
If is an
matrix and
is an
matrix, the dimensions of
are
.
In this problem, If is a
matrix and
is a
matrix, so
the dimensions of are
.
Example Question #34 : Matrices
Find the product .
,
cannot be multiplied
If is an
matrix and
is an
matrix,
can only be multiplied if
, or the number of columns in
equals the number of rows in
. Otherwise there is a mismatch, and the two matrices can not be multiplied.
will be an
matrix
Since is a
matrix and
is a
matrix, then
can be multiplied and will have the dimensions
.
To find the product , you must find the dot product of the rows of
and the columns of
,
We find by finding the dot product of the row
of
and column
of
.
We find by finding the dot product of the row
of
and column
of
.
We use the same method to find the rest of the matrix values
Example Question #35 : Matrix Matrix Product
Find the product .
,
cannot be multiplied
If is an
matrix and
is an
matrix,
can only be multiplied if
, or the number of columns in
equals the number of rows in
. Otherwise there is a mismatch, and the two matrices can not be multiplied.
will be an
matrix
Since is a
matrix and
is a
matrix, then
can be multiplied and will have the dimensions
.
To find the product , you must find the dot product of the rows of
and the columns of
,
We find by finding the dot product of the row
of
and column
of
.
We find by finding the dot product of the row
of
and column
of
.
We use the same method to find the rest of the matrix values
Example Question #31 : Matrix Matrix Product
Find the product .
,
cannot be multiplied
If is an
matrix and
is an
matrix,
can only be multiplied if
, or the number of columns in
equals the number of rows in
. Otherwise there is a mismatch, and the two matrices can not be multiplied.
will be an
matrix
Since is a
matrix and
is a
matrix, then
can be multiplied and will have the dimensions
.
To find the product , you must find the dot product of the rows of
and the columns of
,
We find by finding the dot product of the row
of
and column
of
.
We find by finding the dot product of the row
of
and column
of
.
We use the same method to find the rest of the matrix values
Example Question #41 : Matrix Matrix Product
Find the product .
,
cannot be multiplied
If is an
matrix and
is an
matrix,
can only be multiplied if
, or the number of columns in
equals the number of rows in
. Otherwise there is a mismatch, and the two matrices can not be multiplied.
will be an
matrix
Since is a
matrix and
is a
matrix, then
can be multiplied and will have the dimensions
.
To find the product , you must find the dot product of the rows of
and the columns of
,
We find by finding the dot product of the row
of
and column
of
.
We find by finding the dot product of the row
of
and column
of
.
We use the same method to find the rest of the matrix values
Example Question #42 : Matrices
Find the product .
,
cannot be multiplied.
cannot be multiplied.
If is an
matrix and
is an
matrix,
can only be multiplied if
, or the number of columns in
equals the number of rows in
. Otherwise there is a mismatch, and the two matrices can not be multiplied.
will be an
matrix
Since is a
matrix and
is a
matrix,
so
cannot be multiplied.
Example Question #723 : Linear Algebra
Find the product .
,
cannot be multiplied
If is an
matrix and
is an
matrix,
can only be multiplied if
, or the number of columns in
equals the number of rows in
. Otherwise there is a mismatch, and the two matrices can not be multiplied.
will be an
matrix
Since is a
matrix and
is a
matrix, then
can be multiplied and will have the dimensions
.
To find the product , you must find the dot product of the rows of
and the columns of
,
We find by finding the dot product of the row
of
and column
of
.
We find by finding the dot product of the row
of
and column
of
.
We use the same method to find the rest of the matrix values
Example Question #721 : Linear Algebra
Find the product .
,
cannot be multiplied
If is an
matrix and
is an
matrix,
can only be multiplied if
, or the number of columns in
equals the number of rows in
. Otherwise there is a mismatch, and the two matrices can not be multiplied.
will be an
matrix
Since is a
matrix and
is a
matrix, then
can be multiplied and will have the dimensions
.
To find the product , you must find the dot product of the rows of
and the columns of
,
We find by finding the dot product of the row
of
and column
of
.
We find by finding the dot product of the row
of
and column
of
.
We use the same method to find the rest of the matrix values
Certified Tutor
Certified Tutor
All Linear Algebra Resources
