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Q: If two rows of a matrix are interchanged what is true of the resulting determinant?

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The resulting determinate is the negative, or opposite, of the original determinant.

If it is not a square matrix. You cannot invert a square matrix if it is singular. That means that at least one of the rows of the matrix can be expressed as a linear combination of the other rows. A simple test is that a matrix cannot be inverted if its determinant is zero.

The minor is the determinant of the matrix constructed by removing the row and column of a particular element. Thus, the minor of a34 is the determinant of the matrix which has all the same rows and columns, except for the 3rd row and 4th column.

The square matrix have determinant because they have equal numbers of rows and columns. <<>> Determinants are not defined for non-square matrices because there are no applications of non-square matrices that require determinants to be used.

A minor is a determinant and a determinant is a value associated with a square matrix.The matrix from which a minor is calculated is formed from a matrix by removing at least one of its rows or columns.We are discussing matrices of 3 rows and 4 columns. The minimum change one can make is to remove a single column. This can be done in four ways, yielding four minors. Each of these four ways yields a 3x3 matrix. There are nine minors in a 3x3 matrix.Hence, the total number of minors is 4 + 4(9)=40.

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The resulting determinate is the negative, or opposite, of the original determinant.

It is a matrix or a determinant.

If it is not a square matrix. You cannot invert a square matrix if it is singular. That means that at least one of the rows of the matrix can be expressed as a linear combination of the other rows. A simple test is that a matrix cannot be inverted if its determinant is zero.

The minor is the determinant of the matrix constructed by removing the row and column of a particular element. Thus, the minor of a34 is the determinant of the matrix which has all the same rows and columns, except for the 3rd row and 4th column.

When its determinant is non-zero. or When it is a linear transform of the identity matrix. or When its rows are independent. or When its columns are independent. These are equivalent statements.

The square matrix have determinant because they have equal numbers of rows and columns. <<>> Determinants are not defined for non-square matrices because there are no applications of non-square matrices that require determinants to be used.

Matrix derives from Latin "Mater" which means "mother". It was called this because the determinant, which is very central to matrix mathematics, changes when we remove columns or rows, so with simple words it's because a little matrix can be a part of a larger matrix.

The Value of the Determinant becomes 0

In Algebra, the word determinant is a special number which is associated to any square matrix. Like for example, a rectangular array of numbers where the finite number of rows and columns are equal. Therefore, the meaning of a determinant is a scale factor for measuring wherever the matrix is regarded.

A matrix having the same number of rows and columns is a SQUARE MATRIX.

Restate the question: "What is the order of a matrix?" The order of a matrix tells the number of rows and columns in the matrix. For instance, a matrix with 3 rows and 4 columns is a 3x4 matrix ("three by four"). A square matrix has the same number of rows and columns: 2x2

A minor is a determinant and a determinant is a value associated with a square matrix.The matrix from which a minor is calculated is formed from a matrix by removing at least one of its rows or columns.We are discussing matrices of 3 rows and 4 columns. The minimum change one can make is to remove a single column. This can be done in four ways, yielding four minors. Each of these four ways yields a 3x3 matrix. There are nine minors in a 3x3 matrix.Hence, the total number of minors is 4 + 4(9)=40.

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