How to find scalar interactions with a matrix - ACT Math
Card 0 of 36
Evaluate: 
Evaluate:
This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.

This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.
Compare your answer with the correct one above
Simplify:

Simplify:
Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:

The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.


Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:
The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.
Compare your answer with the correct one above

What is
?
What is ?
You can begin by treating this equation just like it was:

That is, you can divide both sides by
:

Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:

Then, simplify:

Therefore, 
You can begin by treating this equation just like it was:
That is, you can divide both sides by :
Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:
Then, simplify:
Therefore,
Compare your answer with the correct one above
If
, what is
?
If , what is
?
Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of
:

Now, this means that your equation looks like:

This simply means:

and
or 
Therefore, 
Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of :
Now, this means that your equation looks like:
This simply means:
and
or
Therefore,
Compare your answer with the correct one above
Evaluate: 
Evaluate:
This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.

This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.
Compare your answer with the correct one above
Simplify:

Simplify:
Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:

The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.


Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:
The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.
Compare your answer with the correct one above

What is
?
What is ?
You can begin by treating this equation just like it was:

That is, you can divide both sides by
:

Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:

Then, simplify:

Therefore, 
You can begin by treating this equation just like it was:
That is, you can divide both sides by :
Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:
Then, simplify:
Therefore,
Compare your answer with the correct one above
If
, what is
?
If , what is
?
Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of
:

Now, this means that your equation looks like:

This simply means:

and
or 
Therefore, 
Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of :
Now, this means that your equation looks like:
This simply means:
and
or
Therefore,
Compare your answer with the correct one above
Evaluate: 
Evaluate:
This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.

This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.
Compare your answer with the correct one above
Simplify:

Simplify:
Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:

The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.


Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:
The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.
Compare your answer with the correct one above

What is
?
What is ?
You can begin by treating this equation just like it was:

That is, you can divide both sides by
:

Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:

Then, simplify:

Therefore, 
You can begin by treating this equation just like it was:
That is, you can divide both sides by :
Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:
Then, simplify:
Therefore,
Compare your answer with the correct one above
If
, what is
?
If , what is
?
Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of
:

Now, this means that your equation looks like:

This simply means:

and
or 
Therefore, 
Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of :
Now, this means that your equation looks like:
This simply means:
and
or
Therefore,
Compare your answer with the correct one above
Evaluate: 
Evaluate:
This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.

This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.
Compare your answer with the correct one above
Simplify:

Simplify:
Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:

The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.


Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:
The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.
Compare your answer with the correct one above

What is
?
What is ?
You can begin by treating this equation just like it was:

That is, you can divide both sides by
:

Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:

Then, simplify:

Therefore, 
You can begin by treating this equation just like it was:
That is, you can divide both sides by :
Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:
Then, simplify:
Therefore,
Compare your answer with the correct one above
If
, what is
?
If , what is
?
Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of
:

Now, this means that your equation looks like:

This simply means:

and
or 
Therefore, 
Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of :
Now, this means that your equation looks like:
This simply means:
and
or
Therefore,
Compare your answer with the correct one above
Evaluate: 
Evaluate:
This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.

This problem involves a scalar multiplication with a matrix. Simply distribute the negative three and multiply this value with every number in the 2 by 3 matrix. The rows and columns will not change.
Compare your answer with the correct one above
Simplify:

Simplify:
Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:

The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.


Scalar multiplication and addition of matrices are both very easy. Just like regular scalar values, you do multiplication first:
The addition of matrices is very easy. You merely need to add them directly together, correlating the spaces directly.
Compare your answer with the correct one above

What is
?
What is ?
You can begin by treating this equation just like it was:

That is, you can divide both sides by
:

Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:

Then, simplify:

Therefore, 
You can begin by treating this equation just like it was:
That is, you can divide both sides by :
Now, for scalar multiplication of matrices, you merely need to multiply the scalar by each component:
Then, simplify:
Therefore,
Compare your answer with the correct one above
If
, what is
?
If , what is
?
Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of
:

Now, this means that your equation looks like:

This simply means:

and
or 
Therefore, 
Begin by distributing the fraction through the matrix on the left side of the equation. This will simplify the contents, given that they are factors of :
Now, this means that your equation looks like:
This simply means:
and
or
Therefore,
Compare your answer with the correct one above