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AP Intermediate 2nd Year Matrices and Determinants — practice questions — page 3

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.

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Matrices and Determinants questions and exercises with answers

Showing questions 61–87 of 87.

For easier work, expand along the row or column with most:Read the answer and worked solution →A determinant of zero means the matrix is:Read 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 →A determinant may be thought of as a function from matrices to:Read 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 →Before finding the inverse of a matrix, we first define its:Read 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 →A square matrix is invertible if and only if it is:Read the answer and worked solution →Match each condition to what it tells youRead the answer and worked solution →Match the determinant termRead 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 →True or false about determinantsRead the answer and worked solution →Singular or non-singular?Read the answer and worked solution →Determinant numbersRead the answer and worked solution →Complete the invertibility ruleRead the answer and worked solution →A determinant can be associated with which kind of matrix?Read the answer and worked solution →

Worked practice questions

For easier work, expand along the row or column with most:

  1. Onesss
  2. Twosss
  3. Digits
  4. Zeros
Show answer and solution

Correct answer: D. Zeros

1. Each term is multiplied by its element. 2. An element of zero kills its whole term. 3. So expanding along the line with most zeros is easiest. 4. The answer is zeros. _Source: syllabus Mathematics, Ch 4 'Determinants'_

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A determinant of zero means the matrix is:

  1. Singular
  2. Invertible
  3. Symmetric
  4. Rectangle
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Correct answer: A. Singular

1. A matrix with zero determinant has no inverse. 2. Such matrices have their own name. 3. They are called singular. 4. So the answer is singular. _Source: syllabus Mathematics, Ch 4 'Determinants'_

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Symmetric or skew symmetric?

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Items
  1. Item
    A′ = A
    Category
    Symmetric
  2. Item
    Entry (i,j) equals entry (j,i)
    Category
    Symmetric
  3. Item
    A′ = −A
    Category
    Skew symmetric
  4. Item
    Entry (i,j) is the negative of entry (j,i)
    Category
    Skew symmetric
Categories
  1. Item
    Symmetric
  2. Item
    Skew symmetric
One condition is A′ = A, the other A′ = −A, and the chapter notes every square matrix splits into a sum of the two. Source: syllabus Maths Part I, Ch 3 Matrices.

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