Helwan University Faculty Of Engineering Chapter II: Determinants

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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?

$-25$ Signup and view all the answers

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

Using determinants Signup and view all the answers

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

The matrix has no inverse Signup and view all the answers

How is Cramer's Rule related to matrices?

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

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

The number of nonzero elements in A Signup and view all the answers

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

'Determinant' method Signup and view all the answers

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

'Cramer's Rule' Signup and view all the answers

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?

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

How can the rank of a matrix be defined?

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

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

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

How is Cramer's Rule related to matrices?

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

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

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

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