Common Core Standard HSN-VM.C.11 Questions

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Grade 12 Matrices CCSS: HSN-VM.C.11

Let

$vec{v}$ be a vector with 2 or more components and represented as a column matrix, and let

$A$ be a transformation matrix. When the transformation matrix is applied to

$vec{v}$ it results in a new vector,

$vec{w}$ . Which of the following correctly represents this?

$vec{w} = vec{v}A$
$vec{w} = A vec{v}$
$vec{w} = vec{v} A vec{v}$
Both options (a) and (b) are correct.

Grade 12 Matrices CCSS: HSN-VM.C.11

Find the product of

$[[3,-1],[4,-2]]$ and

$<<4,-3>>$ .

These cannot be multiplied together.
$[[9],[10]]$
$[[0,2]]$
$[[15],[22]]$

Grade 12 Matrices CCSS: HSN-VM.C.11

For the vector

$<<3,-1,4>>$ , find the resulting vector if the transformation matrix

$[[3,2,1],[3,2,1],[3,2,1]]$ is applied to it.

$[[11],[11],[11]]$
$[[18],[12],[6]]$
$[[13],[13],[13]]$
This vector and matrix cannot be multiplied together.

Grade 12 Matrices CCSS: HSN-VM.C.11

For the transformation matrix

$A = [[1,0],[0,-1]]$ , how is the vector

$vec{v} = <<3, 4>>$ affected if it is multiplied with

$A ?$

It has been rotated 90° clockwise.
It has reversed direction.
It has been reflected over a horizontal line.
The resulting transformation is a combination of reflections and rotations.

Grade 12 Matrices CCSS: HSN-VM.C.11

For the matrix

$A = [[1,0,0],[0,1,0],[0,0,0]]$ , what is the best description of how this transforms a vector with 3 components if they are multiplied together?

The vector stays the same.
The vector now only has 2 components.
The vector's third component is changed to zero.
At least one component of the vector is reduced to zero.

Grade 12 Matrices CCSS: HSN-VM.C.11

Which matrix would transform the vector

$<< 4,2,7 >>$ to the vector

$<<20,23,51 >>$ ?

$[[0,3,2],[4,0,1],[3,2,5]]$
$[[3,2,5],[4,0,1],[0,3,2]]$
$[[0,4,3],[3,0,2],[2,1,5]]$
$[[5,1,2],[2,0,3],[3,4,0]]$

Grade 12 Matrices CCSS: HSN-VM.C.11

The matrix

$[[1,2,3],[4,5,6],[7,8,9]]$ multiplied by the vector

$<< 1,2,3 >>$ equals which of the following?

$[[1,4,9],[4,10,18],[7,16,27]]$
$[ [14],[32],[50]]$
$[[12],[30],[54]]$
$[[1,2,3],[8,10,12],[21,24,27]]$

Grade 12 Matrices CCSS: HSN-VM.C.11

What does the matrix

$[[2,6,1],[4,1,8]]$ multiplied by the vector

$<< 4,10,-5 >>$ equal?

$[[8,60,-5],[16,10,-40],[0,0,0]]$
$[ [16,10,-40],[8,60,-5]]$
$[[24],[70],[-45]]$
$[[63],[-14]]$

Grade 12 Matrices CCSS: HSN-VM.C.11

How would the vector

$<< 4,10,-5 >>$ would be represented as a matrix?

$[[4,10,-5],[0,0,0],[0,0,0]]$
$[ [4,0,0],[0,10,0],[0,0,-5]]$
$[[-5],[10],[4]]$
$[[4],[10],[-5]]$

Grade 12 Matrices CCSS: HSN-VM.C.11

How would the vector

$<< 1,4,7 >>$ be represented as a matrix?

$[[1,4,7],[0,0,0],[0,0,0]]$
$[[1],[4],[7]]$
$[[7],[4],[1]]$
$[ [1,0,0],[0,4,0],[0,0,7]]$

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Common Core Standard HSN-VM.C.11 Questions

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