1001 Algebra Problems.PDF

Set 57 (Page 134)

897. b.It is known that if is such that det A= ad– bc≠0, then. Applying

this formula with A= yields the following:

898. a.It is known that if is such that det A= ad– bc≠0, then. Applying

this formula withA= yields the following:

899. a.It is known that if is such that det A= ad– bc≠0, then. Applying

this formula withA= yields the following:

900. a.It is known that if is such that det A= ad– bc≠0, then. Applying

this formula with A= yields the following:

901. d.It is known that if is such that det A= ad– bc≠0, then. Note that

the determinant ofA= >– 21 –^24 His zero, so the matrix does not have an inverse.

A detA

d

c

b

a

1

–

A a –^1 = > – H

c

b

=> dH

A^111

1

3

2

1

1

3

– – 2

––

–

– (^1) ==>>HH

2

1

3

> 1 H

A detA

d

c

b

a

1

–

A a –^1 = > – H

c

b

=> dH

A^113

2

2

1

3

2

2

– – 1

––

–

– (^1) ==>>HH

1

2

2

> 3 H

A detA

d

c

b

a

1

–

A a –^1 = > – H

c

b

=> dH

A ab b a a

b

1

0

0

1

0

0

1

– (^1) ==

R

T

S

S

S

S

>

V

X

W

W

W

W

H

a

0 b

>^0 H

A detA

d

c

b

a

1

–

A a –^1 = > – H

c

b

=> dH

A^1 –^122 –^51 – – 37 –^22

5

221

227

223

– ==>>HH

3

1

7

5

>– H

A detA

d

c

b

a

1

–

A a –^1 = > – H

c

b

=> dH

ANSWERS & EXPLANATIONS–