OEF Déterminant
--- Introduction ---
Ce module regroupe pour l'instant 26 exercices sur le déterminant
d'une matrice carrée.
det 2x2
Compute the determinant of the matrix
det 3x3
Compute the determinant of the matrix
det 4x4
Compute the determinant of the matrix
det 5x5
Compute the determinant of the matrix
Determinant and rank
Let
and
be two matrices ×, such that and . Then
. (You should put the most relevant reply.)
Det and trace 2x2
Compute the determinant and the trace of the matrix
Det and trace 3x3
Compute the determinant and the trace of the matrix
Det and trace 4x4
Compute the determinant and the trace of the matrix
Example 2x2
Find a matrix
such that: - All the coefficients
are integers 0;
- det(A) 0.
Example 2x2 II
Find a matrix
such that: - All the coefficients
are integers 0 ;
- det(A) 0 ;
-
= .
Example 2x2 IIb
Find a matrix
such that: - All the coefficients
are integers 0 ;
- det(A) 0 ;
-
.
Example 2x2 III
Find a matrix
such that: - All the coefficients
are integers ;
- det(A) 0 ;
- The product
= .
Example 2x2 IIIb
Find a matrix
such that: - All the coefficients
are integers 0 ;
- det(A) 0 ;
-
;
-
.
Gauss 3x3
Let A be a 3×3 matrix. We make a series of operations on A: - Replace number by the sum of times number plus times number .
- number by .
- Replace number by the sum of times number plus times number .
- Exchange number and .
After these operations, the matrix becomes
. What is the determinant of A ?
Gauss 3x3 II
Let A be a 3×3 matrix with det(A) = . We make a series of operations on A: - Replace number by the sum of times number plus times number .
- number by .
- Replace number by the sum of times number plus times number .
- Exchange number and .
After these operations, we obtain a new matrix B. What is its determinant?
Given products
Let A and B be two × matrices of real coefficients. Given that
and
, what are the determinants of A and B ?
Parametric 3x3
For which value of the parameter t do we have det
= ?
Parametric 4x4
For which value of the parameter t do we have det
= ?
Row permutation 3x3
Consider the following matrices.
Given that det(A) = , what is det(B) ?
Row permutation 3x3 II
Consider the following matrices.
Given that det(A) = , what is det(B) ?
Product and inverse 2x2
Let A and B be two × matrices. Given that
, what is the determinant of A?
Product and inverse 3x3
Let A and B be two × matrices. Given that
, what is the determinant of A?
Product and inverse 4x4
Let A and B be two × matrices. Given that
, what is the determinant of A?
Product and inverse 5x5
Let A and B be two × matrices. Given that
, what is the determinant of A?
Addition of rows
Let A b a × matrix with det(A) = . If we replace the number of A by the sum of times number plus times number , we obtain a new matrix B. What is its determinant?
Addition of rows II
Let A be a × matrix. If we replace the number of A by the sum of times number plus times number , we obtain a new matrix B. Given that det(B) = , what is the determinant of A ?
D'autres exercices sur :
Matrice
Déterminant
Algèbre linéaire
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