Let a be an n × n real matrix and the whole of the polynomial f (a) with real coefficients of A. for the addition and multiplication of matrices, we try to prove that it is a linear space Urgent!

Let v = {f (a) | f (x) be a polynomial with real coefficients}
Because the addition and multiplication of matrices satisfy the eight laws of linear space,
Therefore, we only need to prove that v-pair operations are closed
For any f (a) and G (a) in V, then H (x) = f (x) + G (x) is a polynomial with real coefficients, so f (a) + G (a) = H (a) also belongs to v
For any real number k, KF (x) is also a polynomial with real coefficients, so KF (a) also belongs to v
So V is a linear space

The coefficient of cubic term in polynomial (x ^ 2-8x + 7) (x ^ 2-x) is?

1*(-1)+(-8)*1=-9

In the square + y of the polynomial 2x / 3, the coefficient of the quadratic expression is

The square of the first term x is quadratic and the coefficient is 2 / 3

How many ten thousand tons of water is ten thousand cubic meters of water

Ten thousand tons of water, one cubic meter of water is one ton of water

The 999 power of N divided by 999 is an integer. How many times is n like this?
N must be a positive integer!
Sorry, wrong pull, should be n 999 power + 1 divided by 999 as an integer, so how many n?
If not + 1, that's too easy!
(don't say no, I've only found one so far.)

Countless
For example, n = 998, that is, (999-1) 999 power + 1 can be divisible by 999,
(999-1) 999 power + 1 can be expanded by binomial definition
Each term contains the n power of 999, so it can be divisible by 999
Similarly, n = 999m-1, (M = 1,2,3.) can be divisible by 999

How many tons of water is 10000 liters of water?

1000 liters = 1 cubic meter of water = 1 ton
10 tons

How much is the remainder of 5 divided by 11? Thank you

Because 5 ^ 3 = 125 divided by 11, the remainder is: 4, so: 5 ^ 2001 = (5 ^ 3) ^ 667 divided by 11, the remainder is: 4 ^ 667 divided by 11. Because: 4 ^ 4 = 256 divided by 11, the remainder is: 3, so: 4 ^ 667 = 4 ^ 3 * (4 ^ 4) ^ 166 divided by 11, the remainder is: (4 ^ 3) * (3 ^ 166) divided by 11. Because: 3 ^ 5 = 243 divided by 11, the remainder is: 1, so: 3 ^ 166 = 3 * (3 ^ 5) ^ 33 divided by 11, the remainder is: 3 * (1 ^ 33) divided by 11, So the remainder of 4 ^ 3 * (3 ^ 166) divided by 11 is (4 ^ 3) * 3 divided by 11, which is 5

How many milliliters is a liter of water

1000

What is the remainder of 2001 divided by 11

2001 = (11 * 181 + 10), 2001 * 2001 / 11 = (11 * 181 + 10) * (11 * 181 + 10) / 11 = 11 * 181 * 181 + 2 * 10 * 181 + 100 / 11, so the remainder is 1

How many cubic meters is one kilogram of water

0.001

Let a be an n × n real matrix and the whole of the polynomial f (a) with real coefficients of A. for the addition and multiplication of matrices, we try to prove that it is a linear space Urgent!