Helwan University Faculty Of Engineering Chapter II: Determinants
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Questions and Answers

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

  • $\begin{pmatrix} 83 & -13 & -25 \ -19 & 10 & 7 \ -44 & 12 & 1 \end{pmatrix}$ (correct)
  • $\begin{pmatrix} 4 & 6 & -3 \ 2 & 3 & -4 \ 1 & -2 & 3 \end{pmatrix}$
  • $\begin{pmatrix} 2 & -1 & 3 \ 1 & 9 & -2 \ 4 & -8 & 11 \end{pmatrix}$
  • $\begin{pmatrix} 0 & 6 & -3 \ 1 & -21 & 0 \ 3 & -4 & -25 \end{pmatrix}$

    • What is the general solution of the system provided in the text?

  • $x_1 = 0, x_2 = 2, x_3 = 3$ (correct)
  • $x_1 = -25, x_2 = -25, x_3 = -25$
  • $x_1 = -7, x_2 = 14, x_3 = -13$
  • $x_1 = 1, x_2 = -7, x_3 = 3$

    • How can the rank of a matrix be defined?

  • The number of zeros in the matrix
  • The number of rows or columns of the largest square submatrix with a nonzero determinant (correct)
  • The product of the diagonal elements of the matrix
  • The sum of all elements in the matrix

    • What is the determinant of the matrix A in the given text?

    <p>$-25$</p> Signup and view all the answers

    Which method can be used to find the rank of a matrix?

    <p>Using determinants</p> Signup and view all the answers

    In matrix A, what does it mean if the determinant is zero?

    <p>The matrix has no inverse</p> Signup and view all the answers

    How is Cramer's Rule related to matrices?

    <p>It aids in solving systems of linear equations using determinants</p> Signup and view all the answers

    What does rank(𝐴) represent regarding a given matrix A?

    <p>The number of nonzero elements in A</p> Signup and view all the answers

    What process can be used to find the rank of a 2x2 matrix?

    <p>'Determinant' method</p> Signup and view all the answers

    'Dr.Tarek S.T.Ali' is associated with which concept discussed in the content?

    <p>'Cramer's Rule'</p> Signup and view all the answers

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