TMA 3 MTH 212: LINEAR ALGEBRA II QUESTION AND ANSWER

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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
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