The necessary and sufficient condition for a determinant to be equal to zero is that its row vectors are linearly independent emergency It is proved that the necessary and sufficient condition for a determinant to be equal to zero is that its row (column) vectors are linearly independent

The necessary and sufficient condition for a determinant to be equal to zero is that its row vectors are linearly independent emergency It is proved that the necessary and sufficient condition for a determinant to be equal to zero is that its row (column) vectors are linearly independent

Let the group of column vectors of a be A1, A2,..., an
Determinant of matrix a | a | = 0
Ax = 0 has nonzero solution
There exists a group of numbers x1, X2,..., xn which are not all zero
Make X1A1 + x2a2 +... + xnan = 0
A1, A2,..., an linear correlation
Note: 1

In physics, let's take an example of the balance of two forces, an example of the interaction

Add 8 to a number, multiply by 8, subtract 8, divide by 8, and the result is still 8. Then the number is ()
A. 0B. 1C. 8D. 10

(8 × 8 + 8) △ 8-8, = 72 △ 8-8, = 1

Solving quadratic inequality of one variable (1) x ^ 2 - (a + 2) x + 2A

(1)
x²-(a+2)x+2a

Calculator conversion angle: to know the length of 1000 radians 3, how to calculate the angle with a calculator

2 π radian = 360 degrees,
1 radian = 180 degrees / π,
3 radians = 540 degrees / π = 540 / 3.14 ≈ 171.9745 degrees,

Square of 2008 + 2008-2009 using factorization

Square of 2008 + 2008-2009
=2008×（2008+1）-2009
=2008×2009-2009
=2009×（2008-1）
=2009×2007
=4032063

It is known that the sum of the first n terms of the sequence {an} is Sn, and Sn = 23An + 1 (n ∈ n *); (I) find the general term formula of the sequence {an}; (II) if the sum of the first n terms of the sequence {n | an} is TN, find the general term formula of the sequence {TN}

(I) when n ≥ 2, Sn − 1 = 23An − 1 + 1, when n ≥ 2, an = Sn − Sn − 1 = 23An − 23An − 1, when n ≥ 2, an − 1 = 23An − 23An − 1, when n ≥ 2, an is an equal ratio sequence with the first term of A1 = 3 and the common ratio of q = - 2, an = 3 · (- 2) n-1, n ∈ n * (II) from (I), n | an | = 3N · 2N-1 +n•2n-1）2Tn=3（1•21+2•22+3•23+… +（n-1）•2n-1+n•2n）∴-Tn=3（1+2+22+23+… +2n-1-n•2n）∴−Tn＝3[1−2n1−2−n•2n]∴Tn=3+3n•2n-3•2n

1 × 2 of X + 2 × 3 of X + 3 × 4 of X +... + 2009 × 2010 of x = 2009 to solve the equation

x/(1×2)+x/(2×3)+x/(3×4)...+x/(2009×2010)=2009x[1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2009×2010)]=2009x/(1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010)=2009x/(1-1/2010)=20092009x/2010=2009x=2010

In △ ABC, the equation (1 + X ∨ 2) Sina + 2xsinb + (1-x ∨ 2) sinc = 0 has two unequal real roots, then a is ()
A. Acute angle
B. Right angle
C. Obtuse angle
D. It doesn't exist

（1+x^2)sinA+2xsinB+(1-x^2)sinC=0
(sinA-sinC)x^2+2xsinB+(sinA+sinC)=0
The discriminant is greater than 0
sin²B-4(sinA-sinC)(sinA+sinC)=sin²B-4(sin²A-sin²C)>0
4sin²A

What kind of algorithm structure should be used in the algorithm of finding the approximate root of equation x2-5 = 0 by dichotomy? （　　）
A. Sequential structure B. conditional structure C. cyclic structure D. all of the above

Any algorithm has a sequential structure, and the cyclic structure must contain a conditional structure. ∵ dichotomy uses the cyclic structure. In the algorithm that uses dichotomy to find the approximate root of equation x2-5 = 0, sequential structure, conditional structure and cyclic structure are used