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AP Intermediate 2nd Year Determinants — practice questions — page 2

Explore 87 free Determinants questions in AP Intermediate 2nd Year Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Determinants questions and exercises with answers

Showing questions 31–60 of 87.

Assertion and reason: cofactorsRead the answer and worked solution →Spot the odd oneRead the answer and worked solution →Tap everything the chapter actually definesRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Two true, one false: scope of the chapterRead the answer and worked solution →Match each kind of matrix to its conditionRead the answer and worked solution →Sort each matrix by its shapeRead the answer and worked solution →Tap every matrix that must be squareRead the answer and worked solution →Complete the definition of a matrixRead the answer and worked solution →When is a product defined?Read the answer and worked solution →True or false: transposesRead the answer and worked solution →Symmetric or skew symmetric?Read the answer and worked solution →True or false: matrix algebraRead the answer and worked solution →Complete the equality conditionRead the answer and worked solution →Order the steps: is AB defined, and what order is it?Read the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Special square matricesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Tap every statement true of the identity matrixRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →True or false: inversesRead the answer and worked solution →Complete the scalar multiplication rulesRead the answer and worked solution →Which operation needs matching orders?Read the answer and worked solution →Spot the odd one outRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Assertion and reason: structureRead the answer and worked solution →Order the steps: test whether A is symmetricRead the answer and worked solution →True or false: orders and shapesRead the answer and worked solution →

Worked practice questions

Assertion and reason: cofactors

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Questions
  1. Reason
    That sum is the expansion of a determinant with a repeated row.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    Mixing a row with another row's cofactors gives zero.
  2. Reason
    The adjoint is defined as the transpose of the cofactor matrix.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    adj A must be transposed after building the cofactors.
  3. Reason
    A cofactor carries the sign (−1)^(i+j).
    Verdict
    Both are true; the reason does not explain the assertion.
    Assertion
    A determinant can be expanded along any row.
Both halves are true in the last round, but one does not explain the other. Source: syllabus Maths Part I, Ch 4 Determinants.

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Spot the odd one

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Questions
  1. Items
    1. Determinant
    2. Collinear
    3. Adjoint
    4. Inverse
    Odd item
    Collinear
  2. Items
    1. Singular
    2. |A| = 0
    3. Invertible
    Odd item
    Invertible
  3. Items
    1. Cofactor
    2. Row
    3. Column
    Odd item
    Cofactor
  4. Items
    1. ½
    2. (−1)^(i+j)
    3. 1s in the last column
    Odd item
    (−1)^(i+j)
Grouped by what each object actually is. Source: syllabus Maths Part I, Ch 4 Determinants.

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Tap everything the chapter actually defines

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Questions
  1. Items
    1. Text
      Minor
      Matches the category
      Yes
    2. Text
      Cofactor
      Matches the category
      Yes
    3. Text
      Adjoint
      Matches the category
      Yes
    4. Text
      Singular matrix
      Matches the category
      Yes
    5. Text
      Eigenvalue
      Matches the category
      No
    6. Text
      Rank of a matrix
      Matches the category
      No
    Category
    Defined in this chapter
A check on scope: the 2023 edition of this chapter defines these, and does not cover the older list of determinant properties. Source: syllabus Maths Part I, Ch 4 Determinants.

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