Matrices and Determinants: Rows and Columns
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Questions and Answers

What is the order of the matrix B?

  • 1-by-1
  • 3-by-3
  • 2-by-3 (correct)
  • 2-by-2

    • What is the null matrix of order 1-by-2?

  • [0; 0] (correct)
  • [0; 0; 0]
  • [0 0 0]
  • [0 0]

    • What is the transpose of a matrix A obtained by?

  • Adding the rows with columns
  • Interchanging the rows with columns
  • Multiplying the rows with columns
  • Interchanging the columns with rows (correct)

    • What is a matrix called if each of its entries is 0?

    <p>Both a and b (B)</p> Signup and view all the answers

    What is the order of the transpose of a matrix A, if A is of order 2-by-3?

    <p>3-by-2 (C)</p> Signup and view all the answers

    What is the notation for the transpose of a matrix A?

    <p>At (C)</p> Signup and view all the answers

    What is the value of the base 'e' in theoretical investigations in science and engineering?

    <p>2.7182818 (A)</p> Signup and view all the answers

    In logarithms, what happens when you add the logarithms of two numbers?

    <p>Addition (D)</p> Signup and view all the answers

    What is the result of multiplying logₐ(m) and logₐ(n)?

    <p>logₐ(m) - logₐ(n) (A)</p> Signup and view all the answers

    If logₐ(m) = 2.5 and logₐ(n) = 1.8, what does logₐ(mn) equal to?

    <p>4.3 + 1.8 (D)</p> Signup and view all the answers

    What is the result of 10^3.5621 when evaluated?

    <p>30357.21 (B)</p> Signup and view all the answers

    To find the product of two numbers using logarithms, which rule is illustrated by logₐ(mn) = logₐ(m) + logₐ(n)?

    <p>Rule of Multiplication (D)</p> Signup and view all the answers

    What is the order of matrix A in the given text?

    <p>3-by-3 (B)</p> Signup and view all the answers

    How many columns are there in matrix B?

    <p>3 (B)</p> Signup and view all the answers

    What are equal matrices according to the given text?

    <p>Matrices with equal order and equal corresponding elements (C)</p> Signup and view all the answers

    Which of the following is not a requirement for equal matrices?

    <p>Unequal order (D)</p> Signup and view all the answers

    What is the order of matrix L in the given text?

    <p>Cannot be determined with the given information (A)</p> Signup and view all the answers

    If matrix M has m rows and n columns, how is its order specified?

    <p>m-by-n (A)</p> Signup and view all the answers

    Who prepared logarithm tables using base 'e'?

    <p>John Napier (B)</p> Signup and view all the answers

    Antilogarithm tables were prepared by:

    <p>Jobst Burgi (C)</p> Signup and view all the answers

    What is the scientific notation for the distance from Earth to the Sun, approximately 150,000,000 km?

    <p>$1.5 \times 10^{8}$ km (A)</p> Signup and view all the answers

    Which of the following numbers is not written in scientific notation?

    <p>$0.0008 \times 10^{6}$ (D)</p> Signup and view all the answers

    Who prepared logarithm tables using base 10?

    <p>Henry Briggs (A)</p> Signup and view all the answers

    What is the weight of a hydrogen atom in scientific notation?

    <p>$1.7 \times 10^{-24}$ gm (B)</p> Signup and view all the answers

    In the context of algebraic expressions, what is the product of (4x + 7y) and (16x^2 - 28xy + 49y^2)?

    <p>64x^3 + 343y^3 (C)</p> Signup and view all the answers

    What is the result of (5x - 11y) multiplied by (25x^2 + 55xy + 121y^2) in the given context?

    <p>125x^3 - 1331y^3 (B)</p> Signup and view all the answers

    Given that x + 1 = x, what is the value of x^3 + 3 when x^14 = 1/4?

    <p>488 (A)</p> Signup and view all the answers

    Which expression represents the sum of cubes a^3 + b^3?

    <p>(a + b)(a^2 - ab + b^2) (D)</p> Signup and view all the answers

    What is the factored form of 125x^3 - 1331y^3?

    <p>(5x - 11y)(25x^2 + 55xy + 121y^2) (B)</p> Signup and view all the answers

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