Why is invertible matrix full rank?

The rank of a matrix is defined by the highest order of the nonzero subformula of a matrix. The determinant of an invertible matrix is the highest nonzero subformula (of order n), so it is full rank

RELATED INFORMATIONS

1. How to prove that the rank of the sum of two matrices is not less than the sum of matrix ranks rt Hehe, it's the opposite. It should be no more than
2. On the property of matrix rank If a is m × s matrix, B is s × n matrix, if AB = 0, then R (a) + R (b)
3. Properties of matrix rank 4 If P and Q are reversible, then R (PAQ) = R (a)
4. Properties of the rank of linear algebraic matrix If a matrix has a non-zero r-order subformula, and all R + 1-order subformulas containing this r-order subformula are zero, then the rank of the matrix is R. how to prove its correctness or tell me how to deduce from the definition of matrix rank
5. The rank of a is equal to the rank of its transpose matrix. Is this property applicable to any matrix
6. What are the applications of idempotent matrix
7. Let a be a real symmetric idempotent matrix of order n, that is, a & # 178; = a (1) It is proved that there is an orthogonal matrix Q such that (Q-1) AQ = diag (1,1,...) ,1,0,…… ,0） (2) If the rank of a is r, DET (a-2i) is calculated
8. What is a positive definite matrix? What are the properties of a positive definite matrix? If a is a positive definite matrix, then a [i] [i] must be greater than 0?
9. Is the row rank of a matrix always equal to the column rank and equal to the rank of a matrix? Another problem is that if a matrix A is m rows and N columns, and M
10. The rank of the sum of two matrices is less than or equal to the sum of the ranks of two matrices? How to prove
11. Let a be an M × n matrix, C be an invertible matrix of order n, the rank of matrix A is r, and the rank of matrix B = AC is R1, then () A. R ＞ r1b. R ＜ r1c. R = r1d. The relationship between R and R1 depends on C
12. There is a m × n matrix A whose rank is n, that is to say, its column vectors are independent. How can we prove that the transpose × a of a is an invertible matrix?
13. Let λ = 2 be an eigenvalue of invertible matrix A, then matrix (13a) - 1 must have an eigenvalue equal to______ ．
14. Let the sum of all elements of nonsingular matrix a be 2, then the matrix (1 / 3A ^ 2) ^ - 1 has an eigenvalue equal to () (a) 4 / 3; (b) 3 / 4;
15. Let 2 be an eigenvalue of invertible matrix A, then an eigenvalue of 3A ^ 2 + e is
16. Is the invertibility of (a + b) matrix equal to the invertibility of a + if not, what
17. How to prove that matrix A is invertible if and only if 0 is not the eigenvalue of a GOT IT
18. It is proved that the necessary and sufficient condition of invertibility of matrix A is that its eigenvalues are not equal to zero
19. Let the eigenvalues of the third order invertible matrix a be 1, 2 and 4 respectively, then [i-2a ^ - 1] is equal to It's the value of the determinant,
20. Linear Algebra: there is a problem -- let a = (1,0, - 1) t, matrix A = AAT, n be a positive integer, find the determinant of ae-a ^ n? There is a sentence in the answer: from R (a) = 1, we know that the eigenvalues of a are 2,0,0?