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Poem Commentary - Mid term break

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MATRIX BINOMIALS MATHEMATICS SL TYPE I Natalie Sullivan 000650-042 St. Dominic's International School May 2009 A matrix function such as and can be used to figure out expressions. By calculating and the values of X and Y can be solved for. . By following rules of multiplying matrices, this can be shown as =. Using we can conclude that = or. One can generalize a statement of a pattern that develops as the matrix goes on. The expression is as follows, =. The number 2 in the matrix comes from when the product of is solved for. The value of is twice the value of . The variable n represents what power the matrix is to, such as n = 2, 3, 4. We can now solve for the rest of the values of. = Further values of can be proven by the expression, = can be proven with the same expression by slightly changed. Since and are negative, we much change the expression as to meet the demands of and . ...read more.


Let and where and are constants. Let us use different values of and to calculate the values of . for Solving the first example, we can create an expression that should work. The expression for the value can be written as . The comes from multiplying it with , which is shown earlier on, . The comes from the constant of which we solve the value of and raise it to the n power. Continuing using, will now be solved for, using the expression. The same expression can be used for when , . The comes from multiplying it with as shown earlier, =. comes from the constant of we solve the value of and raise it to the power. Since and need to be different constants, the value of in this example will equal . Keeping in mind what and are, we can now find the expression for . By already having and solved for, the conclusion of , which is ). ...read more.


The outer portions of the matrices are the resulting dimensions when multiplied. For instances, you cannot multiply 2x1 � 2x3 since the inner numbers in bold do not match. The matrices used in all examples for finding general states have all been 2x2, which limits the general statements to only 2x2s. The general statements would not work for a 3x3 or any others besides a 2x2. The general statement is . One would get to this general statement algebraically when multiplying or exponentially. The 2 in the equation is twice as much as the square numbers and that is where the number 2 comes from in the general statement. Since 2 receives less than the power and this is where the section of arrives from in the equation . When , and are given earlier on in the paper from their expressions that were found by solving various problems. An example would be: This is the algebraic step and method for solving the general statement of ?? ?? ?? ?? Natalie Sullivan Candidate Number 000650-042 IB Mathematics SL Type 1 Matrix Binomials 1 | Page ...read more.

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