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JEE Main Matrices and Determinants — practice questions — page 3

Explore 89 free Matrices and Determinants questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Matrices and Determinants questions and exercises with answers

Showing questions 61–89 of 89.

True or false: adjoint and inverseRead the answer and worked solution →Tap every statement that is true of a non-singular matrixRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Complete the area formulaRead the answer and worked solution →True or false: expanding a determinantRead the answer and worked solution →For the system Ax = b, if rank(A) < rank(augmented matrix A|b), the system has:Read the answer and worked solution →Complete the equality conditionRead the answer and worked solution →Tap everything the chapter actually definesRead the answer and worked solution →Which side of the inverse test?Read the answer and worked solution →Two are true, one is notRead the answer and worked solution →Determinant of a 2 × 2 matrixRead the answer and worked solution →Singular or non-singular?Read the answer and worked solution →Order the steps for the area of a triangleRead the answer and worked solution →Symmetric or skew symmetric?Read the answer and worked solution →The transpose of the product (AB)^T equals:Read the answer and worked solution →Order the steps: test whether A is symmetricRead the answer and worked solution →Match each kind of matrix to its conditionRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Flip and pair: symbol with meaningRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →Match each term to its definitionRead the answer and worked solution →Spot the odd oneRead the answer and worked solution →Adjoint and identityRead the answer and worked solution →Match each condition to what it tells youRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Assertion and reason: cofactorsRead the answer and worked solution →Complete the scalar multiplication rulesRead the answer and worked solution →

Worked practice questions

True or false: adjoint and inverse

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Questions
  1. Statement is true
    Yes
    Statement
    A (adj A) = (adj A) A = |A| I.
  2. Statement is true
    Yes
    Statement
    adj A is the transpose of the matrix of cofactors.
  3. Statement is true
    No
    Statement
    Every square matrix has an inverse.
  4. Statement is true
    Yes
    Statement
    If AB = BA = I then B is the inverse of A.
  5. Statement is true
    Yes
    Statement
    (A⁻¹)⁻¹ = A.
  6. Statement is true
    No
    Statement
    A singular matrix still has an inverse.
Each line is a summary bullet, stated straight or bent. Source: syllabus Maths Part I, Ch 4 Determinants.

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Tap every statement that is true of a non-singular matrix

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Questions
  1. Items
    1. Text
      |A| ≠ 0
      Matches the category
      Yes
    2. Text
      A⁻¹ exists
      Matches the category
      Yes
    3. Text
      A (adj A) = |A| I
      Matches the category
      Yes
    4. Text
      |A| = 0
      Matches the category
      No
    5. Text
      A has no inverse
      Matches the category
      No
    Category
    True of a NON-singular matrix
  2. Items
    1. Text
      It carries a factor of ½
      Matches the category
      Yes
    2. Text
      It is zero when the points are collinear
      Matches the category
      Yes
    3. Text
      Its third column is all 1s
      Matches the category
      Yes
    4. Text
      It is always positive before taking modulus
      Matches the category
      No
    5. Text
      It needs four points
      Matches the category
      No
    Category
    True of the AREA determinant of a triangle
Non-singular, invertible and |A| ≠ 0 are three names for one condition. Source: syllabus Maths Part I, Ch 4 Determinants.

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Spot the one that does not belong

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Questions
  1. Items
    1. |A| ≠ 0
    2. A is singular
    3. A⁻¹ exists
    Odd item
    A is singular
  2. Items
    1. Minor
    2. Cofactor
    3. Adjoint
    Odd item
    Adjoint
  3. Items
    1. a₁₁A₂₁ + a₁₂A₂₂ + a₁₃A₂₃
    2. a₁₁A₁₁ + a₁₂A₁₂ + a₁₃A₁₃
    3. |A| by expansion along R₁
    Odd item
    a₁₁A₂₁ + a₁₂A₂₂ + a₁₃A₂₃
Each group is built from one summary bullet. Source: syllabus Maths Part I, Ch 4 Determinants.

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