Common Core Standard HSN-VM.C.10 Questions

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Grade 12 Matrices CCSS: HSN-VM.C.10

Adrian was learning about the identity matrix and multiplicative inverses in math class, and is now working on his homework. He knows that, for a square matrix

$A$ , he can usually find another matrix

$B$ such that

$AB = I$ , where

$I$ is the identity matrix of the same size as

$A$ and

$B$ . Adrian is now considering the matrix

$A = [[3,2],[6,4]]$ . The way he has been finding the multiplicative inverse matrix is to create another matrix

$B = [[a,b],[c,d]]$ . He performs this multiplication, and it yields two systems of equations, as follows.

${{:(3a + 2c , = 1),(6a + 4c, = 0):}$

${{:(3b + 2d , = 0),(6b + 4d, = 1):}$

Adrian realizes that both these systems are inconsistent. Is Adrian's work correct? And if so, what does this imply?

No, Adrian's work is not correct. His entire method for finding multiplicative inverses is wrong.
No, Adrian's work is not correct. Although his general method is OK, he has made a mistake when multiplying the matrices.
Yes, Adrian's work is correct. This means that, in this case, no such B matrix exists, and therefore not all square matrices have a multiplicative inverse.
Yes, Adrian's work is correct. This implies that, in this case, the B matrix must be the zero matrix.

Grade 12 Matrices CCSS: HSN-VM.C.10

What is the determinant of

$[[5,7,-2],[3,0,1],[-9,-7,2]] ?$

-112
-28
98
-98

Grade 12 Matrices CCSS: HSN-VM.C.10

If A is a given square matrix, and it is known that there exists a matrix B such that

$AB=1$ , which of the following would be the most efficient ways to find the matrix B?

Find the inverse of A. This is the matrix B.
Find the transpose of A. This is the matrix B.
Create a matrix B whose elements are variables. Then, perform matrix multiplication with the matrix A, setting each resulting entry equal to one. Solve this system of equations, which will give the elements of matrix B.
Multiply both sides of the equation, on the left, by slight variations of the matrix A. When one of these matrices, multiplied by A, becomes the identity matrix, this is the matrix B.

Grade 12 Matrices CCSS: HSN-VM.C.10

For

$M = [[6,-3],[-2,1]]$ , find

$|M|$ .

-9
16
12
0

Grade 12 Matrices CCSS: HSN-VM.C.10

What is the determinant of

$[[1,-3,4],[6,2,-1],[0,3,5]]$ ?

Grade 12 Matrices CCSS: HSN-VM.C.10

What is the determinant of

$[[15,3],[-6,4]]$ ?

Grade 12 Matrices CCSS: HSN-VM.C.10

The 5x5 identity matrix of looks like which of the following?

$[[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]$
$[[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]]$
$[[0,0,1,0,0],[0,0,1,0,0],[1,1,1,1,1],[0,0,1,0,0],[0,0,1,0,0]]$
A and B

Grade 12 Matrices CCSS: HSN-VM.C.10

What is the determinant of

$[[3,2],[6,4]]$ ?

Grade 12 Matrices CCSS: HSN-VM.C.10

What is the determinant of

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

Grade 12 Matrices CCSS: HSN-VM.C.10

What is the determinant of

$[[1,-3,4],[6,2,-1],[0,3,5]]$ ?

Grade 10 Matrices CCSS: HSN-VM.C.10

Find the inverse of

$A= [[2,3],[7,11]]$ .

Grade 10 Matrices CCSS: HSN-VM.C.10

Evaluate the determinant of

$[[-1, 6], [-2, 5]]$ .

Grade 10 Matrices CCSS: HSN-VM.C.10

Find the inverse of

$A= [[9,3],[5,2]]$ .

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Common Core Standard HSN-VM.C.10 Questions

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