the rank of the matrix or order 4×3 is >3. true or false
Answer (1)
17th Nov, 2021
Hi,
Yes, order and rank <= 3 for 4*3. In order to obtain the rank of your 4 ×3 matrix using its minors, first obtain the determinant of each submatrix of the 4×3 matrix. If one of these determinants is nonzero, you may stop and state that the rank of the 4×3 matrix is 3 . However, if the determinants of these four matrices are all zero, then the rank of the 4×3 matrix is less than 3 . In such a case, proceed to find the determinant of each submatrix. If one of these determinants is nonzero, you can stop and state that the rank of the 4×3 matrix is 2 . However, if all of these submatrices have determinant zero, then you know that the rank of the 4×3 matrix is less than 2 - so it is either zero or one. In such a case, it is easy to determine whether the rank is zero or one: it is zero if the entries of the matrix are all zero, otherwise it is one.
Yes, order and rank <= 3 for 4*3. In order to obtain the rank of your 4 ×3 matrix using its minors, first obtain the determinant of each submatrix of the 4×3 matrix. If one of these determinants is nonzero, you may stop and state that the rank of the 4×3 matrix is 3 . However, if the determinants of these four matrices are all zero, then the rank of the 4×3 matrix is less than 3 . In such a case, proceed to find the determinant of each submatrix. If one of these determinants is nonzero, you can stop and state that the rank of the 4×3 matrix is 2 . However, if all of these submatrices have determinant zero, then you know that the rank of the 4×3 matrix is less than 2 - so it is either zero or one. In such a case, it is easy to determine whether the rank is zero or one: it is zero if the entries of the matrix are all zero, otherwise it is one.
A matrix is said to be of rank zero when all of its elements become zero. The rank of the matrix is the dimension of the vector space obtained by its columns. The rank of a matrix
cannot exceed more than the number of its rows or columns
.
Hope this helps.
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