Machine Learning 1 Linear Algebra Review quiz

 

恭喜！您通过了！

正确
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1。

Let two matrices be

A=[4639],B=[−2−592]

What is A - B?

[21−67]

[611−1211]

[611−67]

正确 

To subtract B from A, carry out the subtraction element-wise.

[411211]

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2。

Let x=⎡⎣⎢⎢2741⎤⎦⎥⎥

What is 3∗x?

[621123]

[23734313]

⎡⎣⎢⎢⎢⎢⎢⎢23734313⎤⎦⎥⎥⎥⎥⎥⎥

⎡⎣⎢⎢621123⎤⎦⎥⎥

正确 

To multiply the vector x by 3, take each element of x and multiply that element by 3.

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3。

Let u be a 3-dimensional vector, where specifically

u=⎡⎣814⎤⎦

What is uT?

⎡⎣418⎤⎦

[814]

正确 

[418]

⎡⎣814⎤⎦

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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.) Do
not add brackets to your answer.

正确回答 

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5。

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

must necessarily hold true? Check all that apply.

A∗B∗A=B∗A∗B

未选择的是正确的 

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

正确 

Even though matrix multiplication is not commutative in general (A∗B≠B∗A for general
matrices A,B), for the special case where A=I, we have A∗B=I∗B=B, and
also B∗A=B∗I=B. So, A∗B=B∗A.

A∗B=B∗A

未选择的是正确的 

A+B=B+A

正确 

We add matrices element-wise. So, this must be true.