(22) Let A be a 100 x 90 matrix, representing an image with 9000 pixels. How many numbers do we need to store for a truncated singular value decompo- sition (TSVD) A = Ak with k = 10 ? (a) 1090 (b) 1900 (c) 1910 (d) 1990 (e) 2018

Respuesta :

Answer:

The correct option is c.

Step-by-step explanation:

Let A be a 100 x 90 matrix.

The order of a matrix is m x n, where, m is number of rows and n is number of columns.

[tex]m=100[/tex]

[tex]n=90[/tex]

It is given that for a truncated singular value decompo- sition (TSVD) [tex]A\approx A_k[/tex] with k=10.

The formula for the number of numbers do we need to store for a truncated singular value decompo- sition (TSVD) [tex]A\approx A_k[/tex] is

[tex]N=k(m+n+1)[/tex]

Substitute k=10, m=100 and n=90 in the above formula.

[tex]N=10(100+90+1)[/tex]

[tex]N=10(191)[/tex]

[tex]N=1910[/tex]

The numbers that are needed to store for a truncated singular value decompo- sition (TSVD) is 1910.

Therefore the correct option is c.