Coursera: Machine Learning-Andrew NG(Week 1) Quiz - Linear Algebra

These solutions are for reference only.

try to solve on your own

but if you get stuck in between than you can refer these solutions

there are different set of questions ,

we have provided the variations in particular question in the end.

read questions carefully before marking

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Linear Algebra

TOTAL POINTS 5

1.

Question 1

Let two matrices be

A=[46​39​],B=[−2−5​92​]

What is A + B?

1 point

[2192]

[611−67]

[6111211]

[211211]

explanation:

= [46​39​]  +  [−2−5​92​]

=[4-26-5​3+99+2​] 
 

= [21​1211​]

2.

Question 2

Let x=$x =$

⎡⎣⎢⎢2741⎤⎦⎥⎥

What is $3 * x$?

1 point

[23734313]

⎡⎣⎢⎢621123⎤⎦⎥⎥

⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢23734313⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

[621123]

explanation:

multiply each element by 3.

3.

Question 3

Let u be a 3-dimensional vector, where specifically

$u=\left[\begin{array}{c}3\\ 5\\ 1\end{array}\right]$

What is $u^\text{T}$?

1 point

⎡⎣351⎤⎦

[153]

[351]

⎡⎣153⎤⎦

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

What is (u transpose * v)?

1 point

5.

Question 5

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

must necessarily hold true? Check all that apply.

1 point

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

$A + B = B + A$

$A * B = B * A$

If $C = A*B$, then C is a 6x6 matrix.

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variations in 5th question:

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

must necessarily hold true? Check all that apply.

If C=A*B, then C is a 3x3 matrix.

$A + B = B + A$If A is the 3x3 identity matrix, then A*B=B*A

$A * B = B * A$A*B*A=B*A*B

A*B=B*A

variations in 4th question:

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

and

what is  ?
(Hint:  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  and .) Do not add brackets to your answer.

reference : coursera