Thẻ ghi nhớ: MAE101-PT2 | Quizlet

Determine whether the matrix is in echelon form, reduced echelon form, or neither.

1 0 7 -7

0 1 1 -9

0 0 0 0

Reduced echelon form

Find all values of m so that the system

x+y+3z=m

-x+3y+2z=3

3x-y+4z=-1

all numbers but 1

A homogeneous linear system of 100 equations in 90 unknowns:

is never inconsistent and may have a unique solution

Find all values of a such that the system

has a non-trivial solution.

Select one:

a. None of the other choices is correct

b. 5

c. All numbers but -3

d. All numbers but 5

e. -3

5

Let A, B be matrices of size 4 x 4. Choose the correct statements:(i) (A-2B)T= AT-2BT(ii) If the (2,3)-entry of A is 5 then the (3,2)-entry of AT is also 5(iii) (2A)T= 16(AT)

Select one:

a. (i), (iii)

b. (i), (ii)

c. None of the other choices is correct

d. Only (i)

e. Only (ii)

(i), (ii)

Which of the followings are true of A and B if AB is a column vector?

(i) B is a column vector

(ii) A is a row vector

(iii) the number of rows in A must equal the number of columns in B.

(i) only

Given . Find the sum of (3,1)-entry and (2,3)-entry of A -1

Select one:

a. 1/2

b. none of the other choices is true

c. 0

d. 1/3

e. 1

1/2

Which of the following statements are true? (assume that all matrices are square matrices of the same size).

(i) If A and B are invertible then AB-1 is also invertible and its inverse is BA-1

(ii) If A and B are invertible then AB-1 is also invertible and its inverse is A-1B

Select one:

a. (i) and (ii)

b. (i)

c. (ii)

d. None of them

(i)

Let be reflection in y = x followed by rotation through . Then T is:

Select one:

a. rotation through

b. Reflection in the Y axis

c. reflection in the X axis

d. None of the other choices is true

Reflection in the Y axis

If abcdefghi=7, find 3a-5g g d ...

Select one:

a. -15

b. 34

c. -21

d. 25

-21

Let A be a square matrix. Choose correct statements:(i) det(-A) = -det(A)(ii) If A has two equal rows, then det(A) = 0(iii) If det(A) = 0, then A has two equal row.

Select one:

a. (ii)

b. (iii)

c. None of the other choices is correct

d. (i) and (ii)

e. (i)

(ii)

Let .Find the values of x so that A is invertible.

Select one:

a. -1

b. All numbers but 1

c. 1

d. None of the other choices is corrrect

e. All numbers but -1

All numbers but 1

Let A and B be 2 x 2 matrices such that det(A) = -7 and det(B) = 4. Find det[(AB)-1].

Select one:

a. -7/4

b. 1/28

c. -1/28

d. None of the other choices is corrrect

e. -4/7

-1/28

Find the eigenvalues of the matrix

Select one:

a. -1; 1; -14

b. -1; 1; 14

c. 1; 1; -14

d. -1; -1; 14

e. None of the other choices is corrrect

a

Determine whether the matrix is in echelon form, reduced echelon form, or neither.

123-7

0018

01-41

Select one:

a. Echelon but not reduced

b. Neither

c. Reduced echelon form

b

Solve the system of equations for x3 .

x1 + x2 + x3 = 7

x1 - x2 + 2x3 = 7

5x1 + x2 + x3 = 11

Select one:

a. -2

b. 1

c. 4

d. 3

e. 2

c

For a system of 4 equations in 5 unknowns, which of the following statements are true?

(i) The system can be inconsistent.

(ii) The system can have a unique solution.

(iii) The system can have infinitely many solutions.

Select one:

a. (i)

b. (i), (ii) and (iii)

c. (i) and (iii)

d. (iii)

c

Find all values of a such that the homogeneous system

x+2y-z=0

x+3y+3z=0

...

has a non-trivial solution.

Select one:

a. All numbers but 2

b. All numbers but -2

c. 2

d. None of the other choices is correct

e. -2

d

Find the entries in the first row of matrix B if 3A-B = 2C, with

, and

Select one:

a. 0, -2, 9

b. 0, 2, -9

c. -1, 3, 3

d. None of the other choices is correct

e. 1, -3, 3

e

Let . Using block multiplication to find A100. Choose the correct answer.

Select one:

a. None of the other choices is correct

b. O

c. A

d. 100A

c

How many of the followings are true about a product AB if A is 4x5 matrix?

(i) B must have four rows and the result will have fives columns.

(ii) B must have five columns and the result will be a square matrix.

(iii) B must have four columns and the result will have fives rows

(iv) B must have five rows adn the result will have four rows.

Select one:

a. 3

b. 2

c. 4

d. 1

e. 0

a

Given ; . Find (2,2)-entry of .

Select one:

a. -10

b. -12

c. 10

d. 12

d

Which of the following statements are true?(i) If A is invertible and you interchange its first two rows to reach B then B is also invertible(ii) If an invertible matrix A commutes with C then A-1commutes with C

Select one:

a. (i)

b. (ii)

c. None of them

d. (i) and (ii)

d

Let be rotation through followed by reflection in the line. Find the matrix of .

Select one:

a.

-10

01

b. all of the other choices are false

c.

10

0-1

d.

11

01

c

Let . Find .

Select one:

a. -40

b. None of the other choices is correct

c. 8

d. -8

e. 40

c

Let A and B be n x n matrices, k a scalar. Choose INCORRECT statements:(i) det(AB)=det(A)det(B)(ii) det(kA)=kdet(A)(iii) det(AT)=det(A)

Select one:

a. (i)

b. (ii)

c. (iii)

d. (i) and (iii)

e. None of the other choices is corrrect

b

Let Find the first row of the matrix adj(A).

Select one:

a. [-15 -2 2]

b. [-15 2 2]

c. [-15 -17 18]

d. None of the other choices is corrrect

e. [-15 17 18]

Let A be a 3 x 3 matrix with det(A-1)=2. Find det [adj(A)].Hint: Use A-1=[1/det(A)].adj(A).

Select one:

a. 1/4

b. None of the other choices is corrrect

c. 4

d. 8

e. 1/8

a

Find the eigenvalues of the matrix

Select one:

a. 2, 3, 7

b. 3, 5, 9

c. -1, -2, 1

d. 0, 0, 4

c

Determine whether the matrix is in echelon form, reduced echelon form, or neither.

167-7

01-4-9

0000

Select one:

a. Neither

b. Echelon but not reduced

c. Reduced echelon form

b

Solve the system of equations for x3

x1 - x2 + 3x3 = -8

2x1 + x3 = 0

x1 + 5x2 + x3 = 40

Select one:

a. -8

b. 0

c. 8

d. 2

b

How many solutions would a homogeneous system of linear equations of 6 equations and in 3 variables have?

Select one:

a. Only one solution

b. Infinitely many solutions

c. 3 solutions

d. No solutions

e. There is not enough information

e

Find the (1, 1) - entry of the matrix A that satisfies

(A^T+2[])^T=3A+7I

Select one:

a. -3

b. 0

c. -2

d. None of the other choices is correct

e. -5

d

Let , . Find (1,2)-entry of matrix AB^T-BA

Select one:

a. None of the other choices is correct

b. 0

c. -5

d. -4

e. -9

c

Let A be 2x10 matrix and let B be 4x5 matrix. Choose the correct statements:

(i) ACB can be performed only if the size of C is 10x4.

(ii) If ACB can be performed then the size of result is 5x2.

Select one:

a. None of the other choices is correct

b. (ii)

c. (i)

d. Both (i) and (ii)

c

Given ; . Find (3,2)-entry of .

Select one:

a. 0

b. 3

c. 1

d. 2

c

Let A, B, C be matrices. Choose INCORRECT statements:(i) If AB=AC then B=C(ii) If A is invertible then (kA)-1=(1/k)A-1, where k is a nonzero number.(iii) If A2 is invertible then A is invertible

Select one:

a. Only (ii)

b. None of the other choices is correct

c. Only (iii)

d. Only (i)

e. (ii) and (iii)

d.

Let T: R2->R2 be reflection in the line followed by rotation through pi/2 . Find the matrix of T.

a.

-10

01

b

1-1

01

c

10

0-1

d

10

-11

a

Let abcpqrxuz. Find 3245x0yz....

Select one:

a. 16

b. -16

c. 8

d. -8

e. none of the other choices is true

a

Let A be a 3 x 3 matrix and B a 4 x 4 matrix. If det A=3 and det B=2 , find det (2A) and det (3B) .

Select one:

a. det (2A)= 48 and det (3B)=36

b. det (2A)= 162 and det (3B)=24

c. det (2A)= det (3B)=6

d. det (2A)= 24 and det (3B)=162

e. None of the other choices is correct

d

Let A=[101010-10x] . Find the values of x so that A is invertible.

Select one:

a. All numbers but 1

b. All numbers but -1

c. -1

d. All numbers but 0

e. 0

f. 1

b

Let A be a 3 x 3 matrix with det(A)=2. Find det [A-1+adj(A)].Hint: Use A-1=[1/det(A)].adj(A).

Select one:

a. 27/2

b. 27/8

c. None of the other choices is correct

d. 3/2

e. 3/8

a

Let A be a 2 x 2 matrix with eigenvalues 2 and 3, and with corresponding eigenvectors [2 1]T and [1 1]T .Find the (1, 2)-entry of A.

Select one:

a. 1

b. None of the other choices is corrrect

c. -1

d. 2

e. 4

d

How many solutions would a system of linear equations of 3 equations and in 6 variables have?

Select one:

a. Only one solutions

b. Infinitely many solutions

c. There is not enough information

d. 3 solutions

e. No solutions

c

Find all values of a such that the system

x+2y+3z=0

4x+ay+6z=0

6x+5y+4z=0

has only the trivial solution.

Select one:

a. None of the other choices is correct

b. 5

c. -3

d. All numbers but -3

e. All numbers but 5

e

Find the (2, 1)-entry of the matrix A that satisfies

Select one:

a. 2

b. -5

c. None of the other choices is true

d. -9/2

e. 7

d

Let , . Find the sum of all entries in second column of the matrix BC.

Select one:

a. 11

b. 21

c. None of the other choices is correct

d. 14

e. 26

d

Let A, B be matrices. Choose correct statements:

(i) If AB=0 then A=0 or B=0

(ii) (A+B)(A-B)=A2-B2

Select one:

a. None of the other choices is correct

b. (ii)

c. (i) and (ii)

d. (i)

a

Find the second entry of the second row of the matrix A that satisfies:

Select one:

a. 1

b. 3

c. 0

d. 2

e. None of the other choices is correct

b

Let A, B, X and C be square matrices. Given that A and B are invertibe and AXB = C. Which of the followings are true?

(i) X = A-1B-1C

(ii) X = CA-1B-1

(iii) X = A-1 CB-1

Select one:

a. (i), (ii) and (iii)

b. (i) only

c. (ii) only

d. None of the other choices is correct

e. (iii) only

e

How many of the following functions are matrix transformation?(i) T(x,y) = (2x+3y; x-y)(ii) T(x,y) = (x+y, 1)(iii) T(x,y) = (x2+y, y)

Select one:

a. 3

b. 1

c. 0

d. none of the other choices is true

e. 2

b

If , find

Select one:

a. 12

b. 24

c. 27

d. 35

a

Let A be a 3 x 3 matrix with det(A)=7. Let:B be the matrix obtained from A by interchanging the first and the second row.C be the matrix obtained from B by dividing the third row by 2.D be the matrix obtained from C by adding 5 times the second row to the third row.Find det(D).

Select one:

a. -14

b. None of the other choices is correct

c. 14

d. 7/2

e. -7/2

e

Let Find the third row of the matrix adj(A).

Select one:

a. [18 20 -36]

b. [2 6 36]

c. None of the other choices is correct

d. [2 -6 -36]

e. [2 6 -36]

b

Let A and B be 2 x 2 matrices such that det(A) = -7 and det(B) = 4.Find det[3A-1 BT].

Select one:

a. -84

b. -36/7

c. -12/7

d. 84

e. None of the other choices is corrrect

b

Let A be a 2 x 2 matrix with eigenvalues 1 and 3, and with corresponding eigenvectors [1 2]T and [1 1]T .Find the (2, 2)-entry of A.

Select one:

a. None of the other choices is corrrect

b. 4

c. -2

d. -1

e. 5

d