Matrices
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Questions and Answers

What is the condition for two matrices A and B to be equal?

  • They have the same number of columns and corresponding elements are equal
  • They have the same number of rows and corresponding elements are equal
  • They have the same number of rows and columns but not necessarily corresponding elements
  • They have the same order and corresponding elements are equal (correct)

    • What is the order of the matrix [5 0 3]?

  • 3×3
  • 3×1
  • 1×1
  • 1×3 (correct)

    • What is the characteristic of a singleton matrix?

  • It has only one row and any number of columns
  • It has only one element (correct)
  • It has only one column and any number of rows
  • It has only one row and one column

    • What is the order of the column matrix [[2][3][−6]]?

    <p>3×1</p> Signup and view all the answers

    What is the notation used to represent the element at the ith row and jth column of a matrix A?

    <p>a_{ij}</p> Signup and view all the answers

    What is the arrangement of numbers enclosed by in a matrix?

    <p>Small or big brackets</p> Signup and view all the answers

    What is the notation used to represent a matrix?

    <p>Capital letters</p> Signup and view all the answers

    What is the condition for a square matrix to be a diagonal matrix?

    <p>All elements of the principal diagonal are non-zero.</p> Signup and view all the answers

    What is the number of zeros in a diagonal matrix of order n × n?

    <p>n^2 - n</p> Signup and view all the answers

    What is the notation for a diagonal matrix of order n × n with diagonal elements d1, d2,..., dn?

    <p>diag[d1, d2,..., dn]</p> Signup and view all the answers

    What is the characteristic of an identity matrix?

    <p>All elements in the main diagonal are one and rest are zero.</p> Signup and view all the answers

    What is a solution of a system of equations?

    <p>A value of x and y that simultaneously satisfy all the equations</p> Signup and view all the answers

    What is a consistent system of equations?

    <p>A system with one or more solutions</p> Signup and view all the answers

    What is the rank of the matrix if x + c ≠ 0?

    <p>3</p> Signup and view all the answers

    What is the matrix representation of the system of linear equations?

    <p>AX = B</p> Signup and view all the answers

    What is a homogeneous system of linear equations?

    <p>A system with a zero constant term</p> Signup and view all the answers

    How many methods are there to solve a non-homogeneous system of linear equations?

    <p>Three methods</p> Signup and view all the answers

    What is an example of a consistent system of linear equations?

    <p>2x + 3y = 5, 4x + 6y = 10</p> Signup and view all the answers

    What is the matrix A in the system of linear equations AX = B?

    <p>The coefficient matrix of the system of linear equations</p> Signup and view all the answers

    What is the echelon form of the matrix?

    <p>A matrix with leading entries in each row</p> Signup and view all the answers

    When is a system of linear equations guaranteed to have an infinite number of solutions?

    <p>When the number of equations is less than the number of unknowns and the system is consistent</p> Signup and view all the answers

    What is the purpose of reducing the augmented matrix to Echelon form in the rank method?

    <p>To solve for the unknowns in a system of linear equations</p> Signup and view all the answers

    What is the relationship between the rank of A and the rank of [A : B] in a system of linear equations AX = B?

    <p>The rank of A is equal to the rank of [A : B] if the system is consistent</p> Signup and view all the answers

    What is the condition for a system of linear equations to have a unique solution?

    <p>The determinant of the coefficient matrix must be non-zero</p> Signup and view all the answers

    What is the purpose of finding the number of non-zero rows in A and [A : B] in the rank method?

    <p>To determine the rank of the matrix</p> Signup and view all the answers

    What is the purpose of reducing the augmented matrix to Echelon form in the rank method?

    <p>To find the solution of the system of linear equations</p> Signup and view all the answers

    What is the condition for a system of linear equations to have a unique solution?

    <p>The number of equations is equal to the number of unknowns</p> Signup and view all the answers

    What is the rank of the matrix A if the system of linear equations AX = B has a unique solution?

    <p>The number of non-zero rows of A</p> Signup and view all the answers

    What is the condition for a system of linear equations to have an infinite number of solutions?

    <p>The number of equations is less than the number of unknowns</p> Signup and view all the answers

    What is the determinant of the matrix A if the system of linear equations AX = B has no solution?

    <p>Zero</p> Signup and view all the answers

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