1001 Algebra Problems.PDF

• MATRIX ALGEBRA–

839.Compute, if possible:

a.

b.

c.

d.This computation is not well-defined.

840.Determine the values ofx, if any exist, that
make the following equality true:

a. 3

b.–3

c. 6

d.There is no such x-value.

841.Determine the values ofx, if any exist, that
make the following equality true:

a.–1 and 1

b.–2 and 2

c.–2

d. 2

842.How many ordered pairs x, y make the follow-

ing equality true:

?

a. 0

b. 1

c. 2

d.infinitely many

843.Determine an ordered pair (x,y)that makes the

following equality true:

a.(–2,–^83 )

b.(2,–^83 )

c.(2,^83 )

d.(–2,^83 )

844.Determine an ordered triple (x,y, z)if one

exists, that makes the following equality true:

a.(1, 1, 1)

b.(0, 1, 1)

c.(0, 0, 0)

d.(0, 1, 0)

845.Which of the following statements is true?

a.The sum of two 42 matrices must be a

4 2 matrix.

b.The sum of a 42 matrix and a 2 4

matrix is well-defined.

c.A constant multiple of a 31 matrix need

not be a 31 matrix.

d.All of the above statements are true.

x

z

yx

z

yx

z

y

3

2

4

2

4

3

4

3

2

4

>>>HH H– = – 0

x

y

2

4

10 6

=> 6 H

32

2

0

2

2

1

42

2

5

43

1

1

x

y

x

– (^42) y

• 
  


• 
  


• 
  


• 
  


• 
  


• ––

  
  

  
  

  HH+

  
  

  
  

  
  

0

1

1

2

1

0

3

3

6

3

xy 6

31–

–

–

=– –

R

T

S

S

S

S

R

T

S

S

S

S

V

X

W

W

W

W

V

X

W W W W 4 x

1 x

31

1

61

–

–

–

–

2

>>HH=

0

2

2

6

0

4

4

x

2

>>––HH=^1

5

2

5

2

0

0

0

5

2

5

2

5

2

5

2

–

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R

T

S S S S S S

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–

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R

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V

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WW