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

byAkshay Daga (APDaga) -يونيو 06, 2021

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▸ Linear Algebra :

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Let two matrices be
$A = \begin{bmatrix} 1 & -4\\ -2 & 1 \end{bmatrix}$ , $B = \begin{bmatrix} 0 & 3\\ 5 & 8 \end{bmatrix}$
What is A - B ?

Let two matrices be
$A = \begin{bmatrix} 1 & -4\\ -2 & 1 \end{bmatrix}$ , $B = \begin{bmatrix} 0 & 3\\ 5 & 8 \end{bmatrix}$
What is A + B ?

Let
$\begin{bmatrix} 8\\ 2\\ 5\\ 1 \end{bmatrix}$
What is 2∗x ?
- $\begin{bmatrix} 16\\ 4\\ 10\\ 2 \end{bmatrix}$
  Correct
  To multiply the vector x by 2, take each element of x and multiply that element by 2.
- $\begin{bmatrix} 16& 4& 10& 2 \end{bmatrix}$
- $\begin{bmatrix} 4& 1& \frac{5}{2}& \frac{1}{2} \end{bmatrix}$
- $\begin{bmatrix} 4\\ 1\\ \frac{5}{2}\\ \frac{1}{2} \end{bmatrix}$

Let
$x = \begin{bmatrix} 5\\ 5\\ 2\\ 7 \end{bmatrix}$
What is 2∗x ?
- $\begin{bmatrix} 10 & 10 & 4 & 14 \end{bmatrix}$
- $\begin{bmatrix} 10\\ 10\\ 4\\ 14 \end{bmatrix}$
  Correct
  To multiply the vector x by 2, take each element of x and multiply that element by 2.
- $\begin{bmatrix} \frac{5}{2}\\ \frac{5}{2}\\ 1\\ \frac{7}{2} \end{bmatrix}$
- $\begin{bmatrix} \frac{5}{2} & \frac{5}{2} & 1 & \frac{7}{2} \end{bmatrix}$

Let u be a 3-dimensional vector, where specifically
$u = \begin{bmatrix} 2\\ 1\\ 8 \end{bmatrix}$
What is $u^{T}$ ?

Let u and v be 3-dimensional vectors, where specifically
$u = \begin{bmatrix} 4 \\ -4 \\ -3 \end{bmatrix}$
and
$v = \begin{bmatrix} 4 \\ 2 \\ 4 \end{bmatrix}$
what is $u^{T}v$ ?
(Hint: $u^{T}v$ 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 $u^{T}$ and $v$ .) Do not add brackets to your answer.
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Let A and B be 3x3 (square) matrices. Which of the following must necessarily hold true? Check all that apply.
- $A*B*A = B*A*B$
- If A is the 3x3 identity matrix, then $A*B = B*A$
  Correct
  Even though matrix multiplication is not commutative in general ( $A*B \neq B*A$ 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, $A*B = B*A$ .
- $A*B = B*A$
- $A+B = B+A$
  Correct
  We add matrices element-wise. So, this must be true.

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.
  Correct
- If A is the 3x3 identity matrix, then $A*B = B*A$
  Correct
  Even though matrix multiplication is not commutative in general ( $A*B \neq B*A$ 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, $A*B = B*A$ .
- $A * B * A = B * A * B$
- $A * B = B * A$

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

▸ Linear Algebra :

Check-out our free tutorials on IOT (Internet of Things):

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