TMA 3 MTH 212: LINEAR ALGEBRA II QUESTION AND ANSWER

TMA 3 MTH 212: LINEAR ALGEBRA II

1. Let T:U ->V be a linear transformation, then rank T + nullity T =______?
   A. Ker V
   B. Ker U
   C. Dim U
   D. Dim V
   The answer is C. Dim U
2. The determinant rank of an m×n matrix A is equal to the ___ of A
   A. Row
   B. Rank
   C. Column
   D. Kernel
   The answer is B. Rank
3. Every matrix can be reduced to row-reduced eachlon matrix by a ____of elementary row operations
   A. Finite sequence
   B. Infinite sequence
   C. Sequence
   D. Series
   The answer is A. Finite sequence
4. The ___ of a row-reduced echelon matrix is equal to the number of its non-zero rows
   A. Row
   B. Rank
   C. Column
   D. Kernel
   The answer is B. Rank
5. The determinant of (2x -x -1/ 2 x 3x/ 1 -1 2)
   A. 2x² + 5x
   B. 2x² + 2x + 20
   C. 7x² + 5x + 2
   D. X² – 5x + 2
   The answer is C. 7x² + 5x + 2
6. T is called ____ if for each vEV, there exists uEU such that TCU) = V
   A. Surjective
   B. Injective
   C. Subjective
   D. Objective
   The answer is A. Surjective
7. What is the determinant rank of the determinant of [1 4/ 2 5/ 3 6]
   A. Zero
   B. 1
   C. 2
   D. 3
   The answer is C. 2
8. The ___ of a row-reduced echelon matrix is equal to the number of its non-zero rows?
   A. Rows
   B. Rank
   C. Column
   D. Kernel
   The answer is B. Rank
9. The determinant [2x -x -1/ 2 x 3x/ 1 -2 3] is?
   A. 2x² + 5x
   B. 2x² + 2x + 20
   C. 7x² + 5x + 2
   D. X² – 5x + 2
   The answer is C. 7x² + 5x + 2
10. Let T : U ->️ V be a linear transformation then rank (T) + nullity T=?
    A. Ker V
    B. Ker U
    C. Dim U
    D. Dim V
    The answer is C. Dim U