U24MA201 Multivariate Calculus and Linear Algebra

The rank of a matrix A is the

• Number of columns in A

• Number of non-zero entries

• Number of non-zero rows in row echelon form

• . Determinant of A

The nullity of a matrix A is defined as

• . Number of rows - rank

• Number of columns - rank

• Rank +1

• Rank x columns

The rank-nullity theorem helps in finding

• Dimension of image

• Determinant

• Eigen value

• Trace of matrix

A transformation is on to if

• Rank= No. of columns

• Rank= No. of rows

• Nullity= No. of columns

• Nullity= No. of rows

Which type of compression removes some information permanently to reduce size?

• Reversible compression

• Lossless compression

• Lossless compression

• Predictive coding

If matrix A is 3 × 3 and nullity(A) = 1, then rank(A) =

• 0

• 1

• 2

• 3

Vectors (1,2) and (2,-1) are:

• Parallel          

• Equal 

• Orthogonal      

• Unit vectors             

• Norm u = Norm V

• 
• u=v

• u=-v

The dot product of two orthogonal vector is:

• 1

• -1

• 0

• 2

• 0

• 1

• 
• 2