# 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
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
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
7. What is the determinant rank of the determinant of [1 4/ 2 5/ 3 6] A. Zero
B. 1
C. 2
D. 3
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
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
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