Start learning →

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

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

Practise Matrices and Determinants with Quill →

Matrices and Determinants questions and exercises with answers

Showing questions 31–60 of 87.

Order the steps to an inverseRead the answer and worked solution →Determinant quick callsRead the answer and worked solution →Assertion and reason: invertibilityRead the answer and worked solution →Since area is positive, we take which value of the determinant?Read the answer and worked solution →Three points are collinear when the determinant of their coordinates is:Read the answer and worked solution →When the area is given and you must find a coordinate, use:Read the answer and worked solution →True or false: cofactor expansionRead the answer and worked solution →Minors and cofactorsRead the answer and worked solution →Order the steps for finding A⁻¹Read the answer and worked solution →Complete the inverse ruleRead the answer and worked solution →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 →A matrix whose determinant is not zero is called:Read the answer and worked solution →The area of a triangle with three collinear points is:Read the answer and worked solution →The minor of an element is found by deleting its:Read the answer and worked solution →The minor of an element in an order n determinant has order:Read the answer and worked solution →The cofactor Aij equals the minor multiplied by:Read 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 →Determinants here are studied up to which order?Read the answer and worked solution →Expanding a determinant along different rows gives:Read the answer and worked solution →

Worked practice questions

Order the steps to an inverse

Read exercise and reference answers
Steps
  1. Find the determinant
  2. Check it is not zero
  3. Work out the cofactors
  4. Form the adjoint
  5. Divide to get the inverse
Instructions
Tap the steps in the order you carry them out.
_Source: syllabus Mathematics, Ch 4 'Determinants'_

Open this exercise →

Determinant quick calls

Read exercise and reference answers
Questions
  1. Question
    Determinant of a matrix with a zero determinant row
    Choices
    1. Zero
    2. One
    3. Undefined
    Correct choice
    Zero
  2. Question
    Order of a minor from an order 4 determinant
    Choices
    1. Four
    2. Three
    3. Five
    Correct choice
    Three
  3. Question
    Best row to expand along
    Choices
    1. Any at random
    2. The longest one
    3. The one with most zeros
    Correct choice
    The one with most zeros
  4. Question
    A matrix with non-zero determinant
    Choices
    1. Non-singular
    2. Singular
    3. Undefined
    Correct choice
    Non-singular
Instructions
Tap the right answer for each case.
_Source: syllabus Mathematics, Ch 4 'Determinants'_

Open this exercise →

Assertion and reason: invertibility

Read exercise and reference answers
Questions
  1. Reason
    A⁻¹ is adj A divided by |A|, and dividing by zero is undefined.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    A matrix with |A| = 0 has no inverse.
  2. Reason
    The determinant used for the area of a triangle vanishes for them.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    Three collinear points enclose no area.
  3. Reason
    The cofactor carries an extra factor of (−1)^(i+j).
    Verdict
    The assertion is false and the reason is true.
    Assertion
    A minor always equals its cofactor.
Tests whether the reason genuinely explains the assertion, not just whether both happen to be true. Source: syllabus Maths Part I, Ch 4 Determinants.

Open this exercise →

How to practise

  1. Choose a Matrices and Determinants question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Matrices and Determinants practice for AP Intermediate 2nd Year. Read explanations as you go. No signup form needed to start.

Practise Matrices and Determinants →

More Mathematics topics

Vector Algebra and 3D GeometryContinuity, Differentiability & DerivativesIntegrals and ApplicationsLinear ProgrammingRelations, Functions & Inverse TrigonometryDifferential EquationsDeterminantsProbability