Assignments 2

Find all values of a such that the homogeneous system

{ x +y +z =0; x -y +3z=0; 3x +y +az = 0 } has a non-trivial solution.

• 2

• 3

• 4

• 5

Let A, B be matrices of size 4 x 4. Choose the correct statements:

(i) (A-2B)T= AT-2BT

(ii) If the (2,3)-entry of A is 5 then the (3,2)-entry of AT is also 5

(iii) (2A)T= 16(AT)

• i

• i+III

• ii

• i+II

How many of the following functions are matrix transformation?

(i) T(x,y) = (2x+3y; x-y)

(ii) T(x,y) = (x+y, 1)

(iii) T(x,y) = (x2+y, y)

• 1

• 2

• 3

• None of the other choices is correct

Let T:R2 ---> R2 be the linear transformation such that

T(1,-1)=(0,1) and T(2,1)=(1,3). Find T(2,3).

• (4/3, 11/3)

• (5/3, 11/3)

• (5/3, 13/3)

• None of the other choices is correct

• 2560

• 2650

• 16000

• 10

• -3 is an eigenvalue

• 2 is an eigenvalue

• 0 and 3 are eigenvalues

• None of the other choices is correct

• 4

• 4/5

• -4

• None of the other choices is correct

• a=1; b=2; c=1

• a=1; b=2; c=-1

• a=1; b=-2; c=1

• a=-1; b=2; c=1

• (0,-1,-2)

• (0,1,-2)

• (0,-1,2)

• None of the other choices is correct

• (8,-6)

• (8, 6)

• (-2, 4)

• (8, -2)