Mathematics

Q1.

(a) --- Left column ---
1. The vector is a linear combination of vectors and . This is true

(b) false

(c) Neither (A) nor (B)

(d) sometimes true and some- times false

Q2.

(a) The set is not a basis set

(b) a basis set Both and (D) None of the above ronstad film del Bith 3. If the mapping is defined as , then is (A) linear (B)

(d) None of the above 03/FH/CC/M-2023-19/169-A --- Right column ---
Let and be the vector spaces
4. over the field and let is a linear transformation from into . If is finite dimensional, then (A) rank – nullity = dim (B) rank + dim = nullity
(C) rank + nullity = dim (D) Both (A) and (B)
5. Let V be the vector space of matrices over R and let . Let be a linear transfor- mation defined by , then the dimension of kernel of is (B) 2 (A) 3 4
6. The characteristic polynomial of the matrix s (A) (B)
(C) (D) \labeleq:3.1 \beginsplit \mathcalL^{\mathcalA}(\mathcalA) = \mathcalL^{\mathcalA}(\mathcalA)\otimes\mathcalL^{\mathcalA}(\mathcalA)\otimes\mathcalL^{\mathcalA}(\mathcalA)\otimes\mathcalL^{\mathcalA}(\mathcalA)\otimes\mathcalL^{\mathcalA}(\mathcalA)\otimes\mathcalL^{\mathcalA}(\mathcalA)\otimes\mathcalL^{\mathcalA}(\mathcalA)\otimes\mathcalL^{\mathcalA}(\mathcalA)\otimes\mathcalL^{\mathcal{