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

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

<p>Using determinants (B)</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 (D)</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 (A)</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 (D)</p> Signup and view all the answers

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

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

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