Matrix - determinant of a matrix and linear system

Translate this into Vietnamese:

An nxn matrix A is invertible if and only if det(A)≠0

• Ma trận cỡ nxn là ma trận khả nghịch nếu det(A)≠0

• Ma trận nxn có thể thay đổi nếu det(A)≠0

• Một ma trận cỡ nxn có thể nghịch đảo nếu det(A)≠0

• Một ma trận cỡ nxn là ma trận khả nghịch khi và chỉ khi det(A)≠0

Translate this into Vietnamese:

If A is invertable

then A^T is invertable and (A^T )^-1=(A^-1 )T

• Nếu A khả nghịch

  thì A khả nghịch và (AT)-1=(A-1)T

• Nếu A nghịch đảo

  thì A khả nghịch và (AT)-1=(A-1)T

• Nếu A khả nghịch

  thì A nghịch đảo và (AT)-1=(A-1)T

• Nếu A nghịch đảo

  thì nghịch đảo và (AT)-1=(A-1)T

Translate this into Vietnamese:

For any square matrix A over F. the polynomial det is the characteristic polynomial of A. The equation det(A- xI) = 0 is equation of A, and the solutions of det (A - xI) = 0 are called the eigenvalues of A. The set of all eigenvalues of A is called the spectrum of A

• Với mọi ma trận vuông A trên F. đa thức det là đa thức đặc trưng của A. Phương trình det(A- xI) = 0 là phương trình của A, và các nghiệm của det (A - xI) = 0 được gọi là các nghiệm của A tập hợp tất cả các giá trị riêng của A được gọi là phổ của A

• Với mọi ma trận vuông A trên F. đa thức det là đa thức đặc trưng của A. Phương trình det(A- xI) = 0 là phương trình của A, và các nghiệm của det (A - xI) = 0 được gọi là các nghiệm của A tập hợp tất cả các giá trị riêng của A được gọi là phổ của A

• Với mọi ma trận vuông A trên F. đa thức det là đa thức đặc trưng của A. Phương trình det(A- xI) = 0 là phương trình của A, và các nghiệm của det (A - xI) = 0 được gọi là các giá trị riêng của A. Tập hợp tất cả các giá trị riêng của A được gọi là phổ của A

• Với mọi ma trận vuông A trên F. đa thức det là đa thức đặc trưng của A. Phương trình det(A- xI) = 0 là phương trình của A, và các nghiệm của det (A - xI) = 0 được gọi là các giá trị riêng của A. Tập hợp tất cả các nghiệm của A được gọi là phổ của A

Fill in the blank number 1:

Carl Friedrich Gauss (1777-1855) was born into a poor working-class family in Brunswick, Germany, and died in Gottingen, Germany, the most famous mathematician in the world. He was a child prodigy with a genius that did not impress his father. However, his teachers were impressed enough to __(1)____ for the Duke of Brunswick to provide a scholarship for Gauss at the local secondary school. As a teenager there, he made original discoveries in number theory and ____(2)_____ to speculate about non-Euclidean geometry. His scientific publications include important contributions in number theory, mathematical astronomy, mathematical geography, ___(3)____, differential geometry and magnetism. In his research Gauss used a method of calculation that later _____(4)____ generalized to row reduction of matrices and named in his honor, although the method was used in China almost 2000 years earlier.

• arrange

• arranges

• arranged

• arranging

Fill in the blank number 2:

Carl Friedrich Gauss (1777-1855) was born into a poor working-class family in Brunswick, Germany, and died in Gottingen, Germany, the most famous mathematician in the world. He was a child prodigy with a genius that did not impress his father. However, his teachers were impressed enough to __(1)____ for the Duke of Brunswick to provide a scholarship for Gauss at the local secondary school. As a teenager there, he made original discoveries in number theory and ____(2)_____ to speculate about non-Euclidean geometry. His scientific publications include important contributions in number theory, mathematical astronomy, mathematical geography, ___(3)____, differential geometry and magnetism. In his research Gauss used a method of calculation that later _____(4)____ generalized to row reduction of matrices and named in his honor, although the method was used in China almost 2000 years earlier.

• begun

• beginning

• began

• had begun

Fill in the blank number 3:

Carl Friedrich Gauss (1777-1855) was born into a poor working-class family in Brunswick, Germany, and died in Gottingen, Germany, the most famous mathematician in the world. He was a child prodigy with a genius that did not impress his father. However, his teachers were impressed enough to __(1)____ for the Duke of Brunswick to provide a scholarship for Gauss at the local secondary school. As a teenager there, he made original discoveries in number theory and ____(2)_____ to speculate about non-Euclidean geometry. His scientific publications include important contributions in number theory, mathematical astronomy, mathematical geography, ___(3)____, differential geometry and magnetism. In his research Gauss used a method of calculation that later _____(4)____ generalized to row reduction of matrices and named in his honor, although the method was used in China almost 2000 years earlier.

• statistics

• statistic

• statistices

• statisties

Fill in the blank number 4:

Carl Friedrich Gauss (1777-1855) was born into a poor working-class family in Brunswick, Germany, and died in Gottingen, Germany, the most famous mathematician in the world. He was a child prodigy with a genius that did not impress his father. However, his teachers were impressed enough to __(1)____ for the Duke of Brunswick to provide a scholarship for Gauss at the local secondary school. As a teenager there, he made original discoveries in number theory and ____(2)_____ to speculate about non-Euclidean geometry. His scientific publications include important contributions in number theory, mathematical astronomy, mathematical geography, ___(3)____, differential geometry and magnetism. In his research Gauss used a method of calculation that later _____(4)____ generalized to row reduction of matrices and named in his honor, although the method was used in China almost 2000 years earlier.

• generation

• generations

• generational

• generators

If the matrix has the same number of rows anf columns, then what type of the matrix is it?

What is the matrix, which consists a single row?

What is the matrix, which is a scalar matrix in which all the diagonal elements are equal to 1 and all the other elements are zero?