What is the Binomial Formula in Matrices without Evaluating Determinants?

In summary, the conversation is about a homework problem involving two matrices and the rule that λ*A = λ*every value in the matrix. The person is unsure of where to start and is looking for help without evaluating the determinants. They are pointed to a rule for adding one column to another column.
  • #1
Crution
10
0

Homework Statement



I'm sorry this doesn't look too nice but it is supposed to be two matricces.

Show:

|1 a1-b1 a1+b1| |1 a1 b1|
|1 a2-b2 a2+b2|=2*|1 a2 b2|
|1 a3-b3 a3+b3| |1 a3 b3|

without evaluating the determinants.

Homework Equations



The Attempt at a Solution



It pretty obviously has got something to do with the 3. binomial formula and the rule that λ*A = λ*every value in the matrix.

I really don't know where to start on this, since I can't evaluate the determinants.
I'm pretty sure there is an easy way to do this, but I just can't see it.

Help is very much appreciated!

Thank you
 
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  • #2
Welcome to PF!

Hi Crution! Welcome to PF! :smile:

Do you know any rules for adding one column to another column? :wink:
 
  • #3
thanks that was enough help :-)
 

Related to What is the Binomial Formula in Matrices without Evaluating Determinants?

1. What is the binomial formula in matrices?

The binomial formula in matrices is a mathematical formula used to expand a binomial expression raised to a power. It is represented as (a + b)^n = a^n + nC1 * a^(n-1)b + nC2 * a^(n-2)b^2 + ... + nCr * a^(n-r)b^r + ... + b^n, where n is the power, a and b are the binomial terms, and nCr represents the combination of n and r.

2. How is the binomial formula in matrices applied?

The binomial formula in matrices is applied by first identifying the values of n, a, and b. Then, the formula is used to expand the binomial expression, including all the terms up to the power of n. The coefficients in the expanded expression can be calculated using the combination formula, nCr = n!/r!(n-r)!, where n! represents the factorial of n.

3. What is the purpose of using the binomial formula in matrices?

The binomial formula in matrices is used to simplify and expand binomial expressions raised to a power. It allows for the easy calculation of coefficients and the expansion of complex expressions. It is also used in various fields of mathematics, such as statistics and probability, to solve problems and make calculations.

4. What are some real-life applications of the binomial formula in matrices?

The binomial formula in matrices has various real-life applications, such as in the field of finance for calculating compound interest, in genetics for predicting the outcomes of genetic crosses, and in physics for solving problems related to projectile motion. It is also used in probability and statistics to calculate the probability of specific outcomes.

5. Are there any limitations of the binomial formula in matrices?

Yes, there are limitations to the binomial formula in matrices. It can only be applied to binomials, which are expressions with two terms. It also assumes that the terms a and b are constant and do not depend on the power n. Additionally, the formula can become complex and time-consuming for higher powers and larger coefficients.

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