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Let the adjoint matrix of matrix A of order n be a *, and prove that: (1) if | a | = 0, then | a * | = 0 What is rank? I haven't learned it, and I can't understand it I can't understand what I've done with the counter evidence If you use the method of disprovement to write down clearly
If | a | = 0, assuming | a * | is not equal to 0, then a * is reversible, that is, (a *) ^ - 1 times a * = E
Then a = AA * (a *) ^ - 1 = | a | (a *) ^ - 1 = 0
That is, a is a 0 matrix, and its adjoint matrix is also a 0 matrix, which contradicts that | a * | is not equal to 0
Get proof
In linear algebra, let a and B be matrices of order n, and a = 1 / 2 (B + I). It is proved that a ^ 2 = a if and only if B ^ 2 = I
Linear Algebra: let a be a matrix of order n × 1, I be an identity matrix, a = I + AA ＾ T, and prove that a is a involution matrix
aa^T=(aa^T)^T
let a=(a1,a2,a3...an),the entry at i-th row and j-th colomn ofaa^T=ai*aj,the same time we have the entry that at j-th row and i-th is aj*ai,which is equal to ai*aj.
I=I^T
=>A=A^T
If the vector a makes the point (3, - 9) move to the point (1,1), find the analytic expression of the image of the function y = 3x ^ 2-12x + 2 after moving according to a?
a=[(1-3),1-(-9)]=(-2,10)
So x becomes X - (- 2) = x + 2
Y becomes Y-10
y-10=3(x+2)²-12(x+2)+2
y=3x²-8
How many cubic meters is one side equal to
What is the unit of a party and how to convert it
One side is the vernacular, which is often said by the people who charge for water. It means cubic meter. They have the same volume, but different quality. Cubic meter is usually used for volume, and cubic meter is usually used for sand
1 m3 = 1 m3
How to solve the square of 5000 (1-x) = 4050?
Square of 5000 (1-x) = 4050
(1-x）²=0.81
1-x = 0.9 or 1-x = - 0.9
x1=0.1,x2=1.9
As shown in the figure, the parabola y = ax2-5ax + 4 passes through the three vertices of △ ABC, the BC ‖ X axis is known, the point a is on the X axis, the point C is on the Y axis, and AC = BC. The analytical formula of the parabola passing through a, B and C is______ ．
According to the meaning of the question: the coordinates of points c, B and a are (0, 4), (x1, 4), (X2, 0). Substituting (x1, 4) into y = ax2-5ax + 4, we get X1 = 5. Because AC = BC, so X22 + 16 = 25, we get x2 = - 3. Substituting (- 3, 0) into y = ax2-5ax + 4, we get a = - 16 ∧ the analytical formula of the parabola passing through three points a, B and C is y = - 16x2 + 56x + 4
Kilogram unit conversion?
4810 kg = how many jin?
How many pairs of men's sole is 1 jin of polyurethane stock solution?
1kg = 1kg = 2kg
4810kg = 9620kg
A mathematics problem about square difference formula
(1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/10^2)
Appendix: square difference formula (a + b) (a-b) = a ^ 2-B ^ 2
11／20
Let f be the focal point of the parabola y ^ 2 = 4x, a and B be two points on the parabola different from the origin, FA and FB are perpendicular, AF and BF are extended and intersected with parabola C and D respectively, and the maximum area of ABCD quadrilateral is obtained
The two straight lines are: y = K (x-1) and KY = 1-x, respectively, and the parabolic equation (because there are two intersections, so K ≠ 0: y = K (x-1) (1) y (x-1) (1) y ^ 2 = 4x. (1) y ^ 2 = 4X. (2) substitute for K ^ 2x ^ 2-2k ^ 2-2k ^ 2x + K ^ 2 (X-1-1) and KY = 1-x, respectively, and the parabolic equation (because there are two intersections, so K ≠ 0, so K ≠ 0: because there are two points, so K \\\\65124; K (there are two points, so K (k, so, so, so, so, so, so, so, so, so k = 0): y = y = y = y = y = K (y = K (x-1): y = K (x-1) (y = K (x-1) (x 2 + 1) / K ^ 2, (1) y ^ 2 = 4x. (2) there are y ^ 2 = 4-4ky, y ^ 2 + 4ky-4 = 0 | y1-1-y1-2-4 = 0 | y1-1-4-4, y ^ 2 = 4-4, y ^ 2 + 2 + 4ky-4 = 4-4ky, y ^ 2 = 4-4ky, y ^ 2 + 2 + 4 = 4-4-4ky, y ^ 2 = 4-4-4-4ky, y ^ 2 = 4-4-4-4-4-4, y-4-1-4, the area of this quadrilateral is s = 0.5l1 * L2 = 0.5l1 * L2 = 0.5l1 * L2 = 0.5 * L2 = 0.5 * L2 = 0.5 * 4 × 4 × 4 (5 * 4 × 4 × 4 (k ^ 4 (K ^ 2 + 4 (k ^ 2 + 4) (k ^ 2 + 4) (k ^ 2 + 4) (k ^ 2 + 4 in this case, the minimum area is 32 and there is no maximum area
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