Question

(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

Answer 1

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.

$m=100$

$n=90$

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

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

$N=k(m+n+1)$

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

$N=10(100+90+1)$

$N=10(191)$

$N=1910$

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

Therefore the correct option is c.