Linear Algebra

1.?

Let two matrices be

A=[4639],B=[?2?592]

What is A - B?

[411211]

[611?1211]

[611?67]

[21?67]

2.?

Let?x=????8251????

What is?2?x?

??????415212??????

[164102]

????164102????

[415212]

3.?

Let u be a 3-dimensional vector, where specifically

u=??814??

What is?uT?

[418]

??814??

??418??

[814]

4.?

Let u and v be 3-dimensional vectors, where specifically

u=???343??

and

v=??315??

What is?uTv?

(Hint:?uT?is a

1x3 dimensional matrix, and v can also be seen as a 3x1

matrix. The answer you want can be obtained by taking

the matrix product of?uT?and?v.)

5.?

Let A and B be 3x3 (square) matrices. Which of the following

must necessarily hold true?

A?B?A=B?A?B

If A is the 3x3 identity matrix, then?A?B=B?A

A+B=B+A

A?B=B?A

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