Machine Learning week 1 quiz: Linear Algebra

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