Question

Why the answer is D? Explain the all process.

23. Which of the following is the expected output of the command below? > X <- matrix(0, 3, 3) > for (i in 1:3) for (j if in 1:3) t ((j-i)<1) { [1, 01 [2,] 1 0 [3,] -2 1 0 2 [1,1 01 [2,]0 01 [3,] 0 0 0 2 [1,] 0 0 0 [2,] 1 00 [3,] 210 [1,] 0 0 0 [2,]0 0 -1 [3,] 0 00 Answer: d

Answer 1

First of all x matrix is defined as :

Now, in the first iteration i = 1 and j = 1

if condition is checked ( j - i ) < 1

( 1 - 1 ) < 1

0 < 1 which is true

Hence, 1^st row and 1^st column element is x[1,1] = ( j - i ) = 1 - 1 = 0

Matrix X remains unchanged.

Now, in the second iteration i = 1 and j = 2

if condition is checked ( j - i ) < 1

( 2 - 1 ) < 1

1 < 1 which is false

Hence, 1^st row and 2^nd column element remains unchanged.

Matrix X remains unchanged.

Now, in the third iteration i = 1 and j = 3

if condition is checked ( j - i ) < 1

( 3 - 1 ) < 1

2 < 1 which is false

Hence, 1^st row and 3^rd column element remains unchanged.

Matrix X remains unchanged.

Now, in the fourth iteration i = 2 and j = 1

if condition is checked ( j - i ) < 1

( 1 - 2 ) < 1

-1 < 1 which is true

Hence, 2^nd row and 1^st column element is x[2,1] = ( j - i ) = 1 - 2 = -1

Matrix X becomes :

$X = \begin{bmatrix} 0 & 0 & 0\\ -1 & 0 & 0\\ 0 & 0& 0 \end{bmatrix}$

Now, in the fifth iteration i = 2 and j = 2

if condition is checked ( j - i ) < 1

( 2 - 2 ) < 1

0 < 1 which is true

Hence, 2^nd row and 2^nd column element is x[2,2] = ( j - i ) = 2 - 2 = 0

Matrix X remains unchanged.

Now, in the sixth iteration i = 2 and j = 3

if condition is checked ( j - i ) < 1

( 3 - 2 ) < 1

1 < 1 which is false

Hence, 2^nd row and 3^rd column element remains unchanged.

Matrix X remains unchanged.

Now, in the seventh iteration i = 3 and j = 1

if condition is checked ( j - i ) < 1

( 1 - 3 ) < 1

-2 < 1 which is true

Hence, 3^rd row and 1^st column element is x[3,1] = ( j - i ) = 1 - 3 = -2

Matrix X becomes :

$X = \begin{bmatrix} 0 & 0 & 0\\ -1 & 0 & 0\\ -2 & 0& 0 \end{bmatrix}$

Now, in the eighth iteration i = 3 and j = 2

if condition is checked ( j - i ) < 1

( 2 - 3 ) < 1

-1 < 1 which is true

Hence, 3^rd row and 2^nd column element is x[3,2] = ( j - i ) = 2 - 3 = - 1

Matrix X becomes :

$X = \begin{bmatrix} 0 & 0 & 0\\ -1 & 0 & 0\\ -2 & -1& 0 \end{bmatrix}$

Now, in the ninth iteration i = 3 and j = 3

if condition is checked ( j - i ) < 1

( 3 - 3 ) < 1

0 < 1 which is true

Hence, 3^rd row and 3^rd column element is x[3,3] = ( j - i ) = 3 - 3 = 0

Matrix X remains unchanged.

So, finally the X matrix is obtained as :

$X = \begin{bmatrix} 0 & 0 & 0\\ -1 & 0 & 0\\ -2 & -1& 0 \end{bmatrix}$