MTH501 TODAY PAPER

Question No: 1 ( Marks: 1 ) - Please choose one
If A is a matrix, the area of the parallelogram determined by the columns of A is

►
► det A

► adj A


Question No: 2 ( Marks: 1 ) - Please choose one
Cramer’s rule leads easily to a general formula for

► the inverse of an matrix A

► the adjugate of an matrix A

► the determinant of an matrix A


Question No: 3 ( Marks: 1 ) - Please choose one
The transpose of an lower triangular matrix is

► lower triangular matrix
► upper triangular matrix

► diagonal matrix

Question No: 4 ( Marks: 1 ) - Please choose one
The transpose of an upper triangular matrix is

► lower triangular matrix
► upper triangular matrix

► diagonal matrix


Question No: 5 ( Marks: 1 ) - Please choose one
Let A be a square matrix of order with , then

► 168
► 186
► 21
► 126

Question No: 6 ( Marks: 1 ) - Please choose one
A basis is a linearly independent set that is as large as possible.

► True
► False


Question No: 7 ( Marks: 1 ) - Please choose one
Let A be an matrix. If for each b in the equation Ax=b has a solution then

► A has pivot position in only one row (may be this option is true)

► Columns of A span
► Rows of A span



Question No: 8 ( Marks: 1 ) - Please choose one
Reduced echelon form of the matrix is

►
►
►
►

Question No: 22 ( Marks: 3 )

find that is invertible or not T(X1,X2)=T(6X1 +8X2 , 5X1 -8X2)

Question No: 23 ( Marks: 3 )

Find the volume of parallelogram of the vertices (1,2,4) (2,4,-7) and (-1,-3,20


Question No: 24 ( Marks: 2 )
Which of the following is true? If V is a vector space over the field F.(justify your answer)

(a)
(b)
(c)


Question No: 25 ( Marks: 5 )
Let is this in R3 or not?


Question No: 26 ( Marks: 5 )
Justify that A2=I if A= , if and only M2=I. justify your answer by portioned matrix of M
M=