Start learning →

AP Intermediate 2nd Year Matrices and Determinants — practice questions

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 1–30 of 87.

By Cramer's rule, the value of x_1 in Ax = b (where A is non-singular) is:Read the answer and worked solution →The transpose of $A^T$ is:Read the answer and worked solution →Tap every statement true of the identity matrixRead the answer and worked solution →A matrix A has an INVERSE if and only if:Read the answer and worked solution →Special square matricesRead 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 →Assertion and reason: structureRead the answer and worked solution →True or false: orders and shapesRead the answer and worked solution →Matrix multiplication is:Read the answer and worked solution →The CHARACTERISTIC EQUATION used to find eigenvalues of matrix A is:Read 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 →When is a product defined?Read the answer and worked solution →True or false: transposesRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →True or false: inversesRead the answer and worked solution →Reading the definitions backRead the answer and worked solution →An ORTHOGONAL matrix A satisfies:Read the answer and worked solution →Which operation needs matching orders?Read the answer and worked solution →The determinant of the 2×2 matrix [[a, b], [c, d]] equals:Read the answer and worked solution →Complete the definition of a matrixRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →True or false: matrix algebraRead the answer and worked solution →For matrices A (3×2) and B (2×4), the product AB has order:Read the answer and worked solution →If A and B are non-singular of the same order, then AB is:Read the answer and worked solution →For a 2 by 2 matrix with A = 2B, det A is det B times:Read the answer and worked solution →Determinants bingoRead the answer and worked solution →Two true, one false: scope of the chapterRead the answer and worked solution →If A = kB for square matrices of order n, then det A equals:Read the answer and worked solution →

Worked practice questions

By Cramer's rule, the value of x_1 in Ax = b (where A is non-singular) is:

  1. $\det(A)/\det(A_1)$ (inverted)
  2. $\det(A_1)/\det(A)$ (correct ratio)
  3. $A_1 \cdot b$ (dot product)
  4. $\det(b)/\det(A)$ (b as matrix)
Show answer and solution

Correct answer: B. $\det(A_1)/\det(A)$ (correct ratio)

**Cramer's rule:** x_i = det(A_i)/det(A), where A_i is the matrix A with the i-th column replaced by b. Requires det(A) ≠ 0 for unique solution.

Open this question →

The transpose of $A^T$ is:

  1. $A$, since transposing twice returns the original on chart
  2. $A^{-1}$, the inverse of the matrix on the school chart
  3. $-A$, the negative of the original matrix here always
  4. $2A$, twice the matrix value on the school chart here
Show answer and solution

Correct answer: A. $A$, since transposing twice returns the original on chart

$(A^T)^T = A$, transposing twice returns the original.

Open this question →

Tap every statement true of the identity matrix

Read exercise and reference answers
Questions
  1. Items
    1. Text
      Diagonal entries are all 1
      Matches the category
      Yes
    2. Text
      Off-diagonal entries are all 0
      Matches the category
      Yes
    3. Text
      It is a square matrix
      Matches the category
      Yes
    4. Text
      All its entries are 1
      Matches the category
      No
    5. Text
      It is the zero matrix
      Matches the category
      No
    Category
    True of the identity matrix I
The identity is the multiplicative anchor of the whole chapter. Source: syllabus Maths Part I, Ch 3 Matrices.

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