1001 Algebra Problems.PDF

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

this formula with A= yields the following:

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

this formula with A= yields the following:

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

the determinant ofA= is zero, so the matrix does not have an inverse.

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

the determinant ofA= is zero, so the matrix does not have an inverse.

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

this formula with A= yields the following:

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

this formula with A= yields the following:

A^180

4

2

0

0

– – 0

1 –

21

– ==>>HH^41

0

4

2

> 0 H

A detA

d

c

b

a

1

–

A a –^1 = > – H

c

b

=> dH

A^10

1

1

(^11)

0

1

1

– – – 1

– (^1) ==–

HH

1

1

1

0

–

–

> – H

A detA

d

c

b

a

1

–

A a –^1 = > – H

c

b

=> dH

3

9

2

6

–

> – H

A detA

d

c

b

a

1

–

A a –^1 = > – H

c

b

=> dH

3

3

2

> 2 H

A detA

d

c

b

a

1

–

A a –^1 = > – H

c

b

=> dH

A 11 1

2

0

1

1

2

0

1

–

––

–

––

– (^1) ==>>HH

1

2

0

1

–

> – H

A detA

d

c

b

a

1

–

A a –^1 = > – H

c

b

=> dH

A 21 1

2

1

0 10

– (^1) ==–– –– 21 21

HH

0

2

1

>–– 1 H

A detA

d

c

b

a

1

–

A a –^1 = > – H

c

b

=> dH

ANSWERS & EXPLANATIONS–