Matrices Bridge Course

Multiple Choice

What is a Matrix?

• An equation of over 5 numbers or symbols 

• A set of numbers in rows and columns

• A method of finding the n^th value of a series

• A complicated number system

Multiple Choice

What must be true in order to ADD two matrices?

• They must be square.

• The dimensions must be equal.

• The determinant can't equal 0.

• The column of the 1st must equal the row of the 2nd.

Multiple Choice

What comes first in the order?

• Row

• Column

Multiple Choice

You can multiply a 2X3 matrix by which matrix?

• 2X2

• 2X12

• 3X12

• 2X3

Multiple Choice

How would a scalar multiplication be carried out for a matrix?

• Add the Scalar to every element in the matrix

• Dot product the rows of one matrix with the columns of the other matrix

• Multiply every element with the scalar to create a new matrix

• subtract the elements in the first matrix from the elements of the second matrix

Multiple Choice

What comes first in the order?

• Row

• Column

Multiple Choice

Diagonal matrix is

• a matrix all the elements except the principal diagonal are zero

• If all the elements above the principal diagonal are zero

• square matrix all the elements except the principal diagonal are zero

• If all the elements below the principal diagonal are zero

Multiple Choice

The value of a _____ does not change when rows and columns are interchanged.

• matrix

• determinant

• linear space

• none of the above

Multiple Choice

Add

• 11    8
  -4     2

• 3     2
  -6    -6

• -3    2
  -4    -6

• 10    8
  -6    2

Multiple Choice

If A is an  SYMMETRIC MATRIX, then

$$A^T=$$  

• A

• $$A^{-1}$$  

• -A

• $$-A^T$$  

Multiple Choice

Dadas las siguientes matrices. Calcule a+b

• Ninguna

Multiple Choice

If A is an  SKEW -SYMMETRIC MATRIX, then

$$A^T=$$  

• A

• $$A^{-1}$$  

• -A

• $$-A^{-1}$$  

Multiple Choice

Add

• 11    8
  -4     2

• 3     2
  -6    -6

• -3    2
  -4    -6

• 10    8
  -6    2

Multiple Choice

If A is a 2 × 3 matrix, and B is a 3 × 4 matrix, how many columns does AB have?

• 2

• 3

• 4

• AB is not defined

Multiple Choice

Subtract

• 3    -8
  0   -1
• 3   -4
  8  -13
• -3   8
  0    1
• 3   -8
  -8    1

Multiple Choice

• 2x3

• 3x2

• 3x4

• 4x3

Multiple Choice

Find A-B

• -3     1
  7     -1
• 1     0
  1     -4
• -4       0
  6     -1
• not possible because rows do not match columns

Multiple Choice

What is a₂₃

• 14

• 4

• 1

• 3

Multiple Select

Al multiplicar 2 matrices, una matriz A de orden 2x3 con una matriz B de orden 3x4 (A*B) , se obtendrá una matriz C de orden:

• 3x4

• 2x3

• 2x4

• No se puede obtener.

Multiple Choice

BA=

• Undefined

Multiple Choice

Multiply

• 20     15    -10
  30     -5         0
• -20      15     -10
  30     -5          0
• 1        8       3
  11     4        5
• 20     -15     10
  -30         5        0  

Multiple Choice

What must be true in order to ADD two matrices?

• They must be square.
• The dimensions must be equal.
• The determinant can't equal 0.
• The column of the 1st must equal the row of the 2nd.

Multiple Choice

An identity matrix is

• If number of columns and rows are equal

• A matrix obtained by interchanging its rows and columns

• If number of columns and rows are not equal

• A square matrix whose diagonal elements are unity and all other elements are zero

Multiple Choice

What do w, x, y and z equal in this matrix equation?

• w = 13, x = 4, y = 7, z = 23

• w = 13, x = -4, y = 11, z = 23

• w = 13, x = 4, y = 11, z = 23

• w = 13, x = 4, y = 11, z = 17

Multiple Choice

Can the operation be performed?

• Yes
• No
• Sometimes
• only Mrs. Jordan knows

Multiple Choice

Matrices can be multiplied only...

• if the row of the first matrix is equal to the column of the second matrix.

• if the column of the first matrix is equal to the column of the second matrix.

• if the column of the first matrix is equal to the row of the second matrix.

• if the row of the first matrix is equal to the row of the second matrix.

Multiple Choice

What would be the dimension of the matrix product AB?

If A_1X4 and B_4X7

• 1X7

• 4X4

• 4X7

• 7X1

Multiple Choice

How many columns are in a 5 x 4 matrix?

• 5
• 4
• 20
• 9

Multiple Choice

Inverse of a square matrix is ____ if it exists

• different

• exists

• unique

• none of the above

Multiple Choice

Find the inverse of the matrix.

• No Inverse Exists

Multiple Choice

• A
• B
• C
• D

Multiple Choice

What is the area of triangle XYZ with vertices X(8,-6), Y(-4,2) and Z(-18,-12)?

• 280

• 140

• 180

• 240

Multiple Choice

Para sumar dos matrices ......

• Tienen que tener el mismo orden

• No importa el orden de las matrices

• Tienen que tener diferente orden

Multiple Choice

If a system has infinite solutions, then it means:

• The lines or planes don't intersect.
• The lines or planes are parallel.
• The lines or planes intersect at a line.
• You get 0=some number when solving the system.

Multiple Choice

What are the ORDER of this matrix?

• 2 x 3

• 3 x 2

• 6 x 1

• 1 x 6

Multiple Choice

if the points A(3,-2),B(k,2) and C(8,8) are collinear,then the value of k is:

• 2

• -3

• 5

• -4

Multiple Choice

To reduce a matric into normal form of the matrix, one can use --------- transformation.

• Row only

• Column only

• Both Row and Column

• Both row or column or both

Multiple Choice

• n = p

• n = p, m =q

• m = n = p = q

• m = q

Multiple Choice

Find 2A-3B

• -3 1

  7 -1

• 1 0

  1 -4

• -4 0

  6 -1

• -14 -5

  11 -3

Multiple Choice

• 0

• I₂

• -I₂

• none of these

Multiple Choice

• (3,7)

• (5,14)

• (9,14)

• (3,14)

Multiple Choice

Evaluate the determinant of the matrix.

• -21

• 0

• 9

• 12

Multiple Choice

• unit matrix

• null matrix

• symmetric matrix

• skew symmetric matrix

Multiple Choice

Find A+B

• 8     10
  8      1 
• 12     25
  7     1
• 10     30
  0     1
• can't add two together because the rows dont match columns

Multiple Choice

• 1/3

• 3

• 5

• 1

Multiple Choice

Calculate the determinant.

• 0

• -15

• -70

• 10

Multiple Choice

• 1

• 1/2

• $$\sqrt{3}$$ /2

• none of these

Multiple Choice

• $$Independent\ of\theta\ only$$

• $$Independent\ of\phi\ only$$

• $$Independent\ of\ both\ \theta\ \ and\ \phi$$

• $$Dependent\ of\ both\ \theta\ \ and\ \phi$$

Multiple Choice

When solving a system AX=C using inverse matrices, you use the equation:

• X=A^-1C

• C=X^-1A

• A=X^-1C

• X=C^-1A

Multiple Choice

A matrix has rank r if

• i) It has at least one non-zero minor of order r

• ii) Every minor of order higher than r vanishes.

• both (i) and (ii)

• none of these

Multiple Choice

Find the product of the two matrices.

• Undefined

• Identity Matrix

Multiple Choice

Find -3A

• Does Not Exist

Multiple Choice

If A be any square matrix,then AA' and A'A will be both

• Skew symmetric

• symmetric

• either skew symmetric or symmetric

• neither skew symmetric nor symmetric

Multiple Choice

Subtract

• -5
  -8
  3
  10
• -9
  8
  3
  2
• 5
  -8
  3
  10
• -5
  8
  3
  2

Multiple Choice

You can multiply a 2X3 matrix by which matrix?

• 2X2
• 2X12
• 3X12
• 2X3

Multiple Choice

Methods to find rank of a matrix

• By calculating non-zero minors

• By triangular form

• By echelon form

• By normal form

• All of the above

Multiple Choice

What do w, x, y and z equal in this matrix subtraction?

• w = 13, x = 4, y = 7, z = 23
• w = 13, x = -4, y = 11, z = 23
• w = 13, x = 4, y = 11, z = 23
• w = 13, x = 4, y = 11, z = 17

Multiple Choice

Rank of the matrix is

• 1

• 2

• 3

• zero

Multiple Choice

Transpose of an orthogonal matrix is ______

• symmetric

• skew symmetric

• hermitian

• orthogonal

Multiple Choice

The equation |A-λI|=0 is called the

• characteristic equation

• characteristic polynomial

• characteristic matrix

• eigen values

Multiple Choice

What do m, n, p and q equal in this scalar matrix multiplication?

• m=8, n=9, p=-4, q=4 
• m=15, n = -45, p=20, q=-5
• m=20, n=-5, p=15, q=-45
• m=-5, n=20, p=-45, q=15

Multiple Choice

Non – trivial solution X of the equation AX=λX is called

• i) Eigen values

• ii) Eigen vectors

• both (i) and (ii)

• none of these

Multiple Choice

A square matrix A= $$\left[a_{ij}\right]_{n\times n}$$  is _______ iff  $$\overline{a_{ij}}\ =a_{ji}$$  

• skew hermitian

• symmetric

• skew symmetric

• hermitian

Multiple Choice

 ¿ Cuál es la traspuesta de la matriz 

Multiple Choice

Elige la respuesta correcta:

• Es una matriz de orden 3x1

• Es una matriz de orden 1x3

• Es una matriz de orden 1x1

• Todas son correctas

Multiple Choice

The eigen values for the matrix

• 4,1

• 4,-1

• 6,1

• 6, -1

Multiple Choice

hallar la traza de la siguiente matriz:

• 6

• 8

• -3

• 11

Multiple Choice

What are the dimensions of this matrix?

• 2 x 3
• 3 x 2
• 6 x 1
• 1 x 6

Multiple Choice

La traza de la matriz es:

• 4

• 42

• 40

• no tiene traza

Multiple Choice

Cayley-Hamilton's theorem is

• The product of the characteristic roots of a square matrix of order n is equal to the determinant of the matrix.

• Every square matrix satisfies its own characteristic equation.

• For a square matrix A. λ is a characteristic root iff there exists a nonzero vector X such that AX=λX.

• The characteristic roots of a real symmetric matrix are all real.

Multiple Choice

The rank of zero matrix is _______

• one

• two

• zero

• three

Multiple Choice

Dadas las siguientes matrices. Calcule C-A

• Ninguna

Multiple Choice

Perform the indicated operation.  If it’s not possible, select Not Possible. 

• 7
  -7
  -6
  20
• 7 
  -9
  -6
  20
• Not Possible
• 7
  -9
  2
  20

Multiple Choice

The rank of every non-singular matrix of order n is _____

• 1

• 0

• 2

• n

Multiple Choice

find: B*A

• 47     30
  9     5
• 17     15
  42     35
• 10     25
  7     1
• not possible because rows do not match columns

Multiple Choice

If A and B are two n-rowed square matrices, then  $$\rho\left(AB\right)---\rho\left(A\right)+\rho\left(B\right)-n$$  

• $$\ge$$  

• $$\le$$  

• $$\ne$$  

• >

Multiple Choice

Multiply

• 20     15    -10
  30     -5         0
• -20      15     -10
  30     -5          0
• 1        8       3
  11     4        5
• 20     -15     10
  -30         5        0  

Multiple Choice

Let AX=B be a system of m linear equations in n variables.If |A|=0 and adj(A).B=0,then the system is __________

• consistent and has unique solution

• consistent and has infinite number of solutions

• inconsistent and has no solution

• none of the above

Multiple Choice

Subtract

• -5
  -8
  3
  10
• -9
  8
  3
  2
• 5
  -8
  3
  10
• -5
  8
  3
  2

Multiple Choice

If in a set of vectors any vector of the set is the linear combination of the remaining vectors, then the vectors are

• linearly independent

• linearly dependent

• data inadequate

• none of the above

Multiple Choice

In Matrix R (pictured) what element is in the second row, third column?

• 8
• 9.01
• 6
• 1

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

What do a, b, c and d equal in this matrix addition?

• a = -1, b = 10, c = 7, d = -11
• a = -1, b = 10, c = -11, d = 7
• a = 10, b = -1, c = 7 , d = -11 
• a = 10, b = -1, c = -11, d = 7