Matrix Jeopardy

Matrix Vocab

100

What does 'kryptos' mean?

hidden

200

To decode a message in cryptograph, you must get the ________ of the given matrix.

inverse

300

A square matrix that is obtained from the identity matrix by a single elementary row operation.

elementary matrix

400

A determinant of the matrix obtained by deleting the ith row and jth column of the given matrix. 

Minor of the element a_ij

500

A matrix that is obtained by transposing the cofactors of the given matrix.

Adjoint

LU, Minor, Cofactor and Adjoint

100

A matrix with only zeros above its main diagonal is called ________ triangular matrix.

Lower

200

Given the matrix,

[ 3  -4 ]

[ 2  -6 ]

find the minor of -6.

3

300

Given the matrix,

[ -6  -2  -1 ]

[  5   1  -6 ] 

[ -4  -6  -6 ]

what is the cofactor of 5? 

-6

400

What is the LU factorization of the following matrix?

[ 2  3 ]

[ 4  9 ]

[ 1  0 ] [ 2  3 ]

[ 2  1 ] [ 0  3 ]

500

What is the adjoint of the following matrix?

[ 2  -1  3 ]

[ 0   5  2 ]

[ 1  -1 -2 ]

[ -8  2  -5 ]

[ -5  -7  1 ]

[ -17 -4  10]

Determinants

100

|5 7|

|3 8|

19

200

If det(A) = 2, what is det(A³)?

2*2*2 = 8

300

Let A be a 3x3 matrix with det(A) = 2 and B = 3A. What is the det(B)?

det(B) = det(3A)

= (3³)*det(A) = 27*2

det (B) = 54

400

Solve for the determinant:

[ -6  -2  -1 ]

[  5   1  -6 ] 

[ -4  -6  -6 ]

170

500

[ l m n ]

[ o p q ]

[ r s t ]

If the determinant of the above matrix is -6, what is the determinant of the following matrix?

[    o       p        q  ]

[ 2l+o 2m+p 2n+q]

[    r        s        t  ]

12

Applications

100

Explain when Cramer's rule will fail when trying to solve a system.

When the determinant of the system is zero. 

200

Given the following system of linear equations,

8x + 7y = -10

-4x - 2y = 8

Using the Cramer's rule, what is the value of D_y?

D_y = 24

300

Determine whether these points A(5, -2), B(4, -1) and C(1, 2) are collinear.

Yes, these points are collinear.

400

Find the area of the triangle given the vertices (1,9), (1,-5), (7,-5).

Area = 42 square units

500

Given the system of linear equations,

-6x + y + 5z = 36

-x + 3y - 4z = -21

2x - 7y + 3z = 18

Using the Cramer's rule, what is the value of D_x?

D_x = -228

MATLAB

100

What MATLAB command will give the determinant of matrix A?

det(A)

200

In MATLAB, what command you should use to get the inverse of matrix A? 

inv(A) or A^-1

300

When solving the system of linear equations using the Gaussian or Gauss-Jordan elimination, what syntax you should use?

rref([A b])

400

When you use the command 'size(A)' in MATLAB, what output will it produce? 

dimensions of matrix A

500

In [A b], what does b represent in the matrix? 

constants in the linear system