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# determinant calculator with variables

From Wikipedia

Calculation

A calculation is a deliberate process for transforming one or more inputs into one or more results, with variable change.

The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm to the vague heuristics of calculating a strategy in a competition or calculating the chance of a successful relationship between two people.

Multiplying 7 by 8 is a simple algorithmic calculation.

Estimating the fair price for financial instruments using the Black-Scholes model is a complex algorithmic calculation.

Statistical estimations of the likely election results from opinion polls also involve algorithmic calculations, but provide results made up of ranges of possibilities rather than exact answers.

To calculate means to ascertain by computing. The English word derives from the Latincalculus, which originally meant a small stone in the gall-bladder (from Latin calx). It also meant a pebble used for calculating, or a small stone used as a counter in an abacus (Latin abacus, Greekabax). The abacus was an instrument used by Greeks and Romans for arithmetic calculations, preceding the slide-rule and the electronic calculator, and consisted of perforated pebbles sliding on an iron bars.

Random variable

In probability and statistics, a random variable or stochastic variable is a variable whose value is not known. Its possible values might represent the possible outcomes of a yet-to-be-performed experiment, or the potential values of a quantity whose already-existing value is uncertain (e.g., as a result of incomplete information or imprecise measurements). Intuitively, a random variable can be thought of as a quantity whose value is not fixed, but which can take on different values; a probability distribution is used to describe the probabilities of different values occurring. Realizations of a random variable are called random variates.

Random variables are usually real-valued, but one can consider arbitrary types such as boolean values, complex numbers, vectors, matrices, sequences, trees, sets, shapes, manifolds, functions, and processes. The term random elementis used to encompass all such related concepts. A related concept is thestochastic process, a set of indexed random variables (typically indexed by time or space).

## Introduction

Real-valued random variables (those whose range is the real numbers) are used in the sciences to make predictions based on data obtained from scientific experiments. In addition to scientific applications, random variables were developed for the analysis of games of chance and stochastic events. In such instances, the function that maps the outcome to a real number is often the identity function or similarly trivial function, and not explicitly described. In many cases, however, it is useful to consider random variables that are functions of other random variables, and then the mapping function included in the definition of a random variable becomes important. As an example, the square of a random variable distributed according to a standard normal distribution is itself a random variable, with a chi-square distribution. One way to think of this is to imagine generating a large number of samples from a standard normal distribution, squaring each one, and plotting a histogram of the values observed. With enough samples, the graph of the histogram will approximate the density function of a chi-square distribution with one degree of freedom.

Another example is the sample mean, which is the average of a number of samples. When these samples are independent observations of the same random event they can be called independent identically distributed random variables. Since each sample is a random variable, the sample mean is a function of random variables and hence a random variable itself, whose distribution can be computed and properties determined.

One of the reasons that real-valued random variables are so commonly considered is that the expected value (a type of average) and variance (a measure of the "spread", or extent to which the values are dispersed) of the variable can be computed.

There are two types of random variables: discrete and continuous. A discrete random variable maps outcomes to values of a countable set (e.g., the integers), with each value in the range having probability greater than or equal to zero. A continuous random variable maps outcomes to values of an uncountable set (e.g., the real numbers). For a continuous random variable, the probability of any specific value is zero, whereas the probability of some infinite set of values (such as an interval of non-zero length) may be positive. A random variable can be "mixed", with part of its probability spread out over an interval like a typical continuous variable, and part of it concentrated on particular values like a discrete variable. These classifications are equivalent to the categorization of probability distributions.

The expected value of random vectors, random matrices, and similar aggregates of fixed structure is defined as the aggregation of the expected value computed over each individual element. The concept of "variance of a random vector" is normally expressed through a covariance matrix. No generally-agreed-upon definition of expected value or variance exists for cases other than just discussed.

## Examples

The possible outcomes for one coin toss can be described by the state space \Omega = {heads, tails}. We can introduce a real-valued random variable Y as follows:

Y(\omega) = \begin{cases} 1, & \text{if} \ \ \omega = \text{heads} ,\\ 0, & \text{if} \ \ \omega = \text{tails} . \end{cases}

If the coin is equally likely to land on either side then it has a probability mass function given by:

\rho_Y(y) = \begin{cases}\frac{1}{2},& \text{if }y=1,\\

\frac{1}{2},& \text{if }y=0.\end{cases}

Question:The following equations are in a bracket. If the determinant is 10, solve for y X+2y+3z= -3 -2x+y-z= 6 3x-3y+2z= -11 I m kinda lost and hope to see someone s work as well so I can fully understand the problem. Thanks!

Answers:Determinants are tricky to do. I'll just give the formula for the determinant of a 3x3 matrix. Given the matrix: | a11 a12 a13 | | a21 a22 a23 | | a31 a32 a33 | The determinant D is given by: D = a11(a22a33-a32a23) +a12(a23a31-a33a21) +a13(a21a32-a31a22). To solve simultaneous equations, first make a matrix of coefficients of the variables: | 1 2 3 | | -2 1 -1 | | 3 -3 2 | Using the above formula, the determinant of this matrix is 15. We can call this determinant D. To solve for any of the three individual variables, first make a matrix consisting of the first matrix, with the column of the variable of interest replaced by the values on the right side of the equal signs. In this case, for y, | 1 -3 3 | | -2 6 -1 | | 3 -11 2 | Again using the formula, the determinant of this matrix is 10, as you were told. We can call this determinant Dy. The answer for y is then Dy/D. In this case, y = Dy/D = 10/15 = 2/3. Similarly, x = Dx/D, and z = Dz/D. Determinants can be a pain, so I usually use the MDETERM() function of MS Excel to quickly evaluate them. I believe most scientific calculators can do determinants too. By the way, x = -3 and z = -2/3.

Question:I am owner financing a real estate sale for 15 years at a fixed interest rate with a required minimum monthly payment of $1,400. The buyer wants to occasionally make larger monthly payments (of variable amounts) and pay it off sooner. Is there an online calculator that will determine balance remaining after each random-amount payment? Answers:yes. but if you do ot know what exart you will be putting it is hard to find it out. but I do have one on my website. www.superdavemortgage.com Question:I want to create a spreadsheet that will calculate the differences in monthly mortgage repayments, based on 2 variables; a) amount borrowed b) interest rate Answers:If A1 has Amount Borrowed B1 has Annual Interest Rate C1 has the Term of loan in Years This calculates the monthly payment =PMT(B1/12, C1*12, -A1) . Question:General rules for entering formulas into a cell: 1.The = sign must precede any formula in Excel. 2.Do not put spaces after the = or between other parts of the formula. 3.The symbol for multiplication is * and for division is / 4.Exponents are written using the ^. For example, c4 becomes c^4. 5.Instead of using an algebraic variable, replace the variable with the name of the cell containing the number to be used. For example, in the formula in cell B3, replace the x with A3. 6.If you do not want the cell name to change as you use Quick Copy, you must anchor the cell name. F4 anchored becomes$F\$4. 7.After finishing the formula, hit Enter. The calculated value will appear in the cell and the formula will appear in the Formula bar at the top. Example You do not have to include this example on your worksheet. The formula for the example is y =3x +5. In cell A2, type x for the column heading, then in cells A3 and A4 put 2 and 4, respectively. Highlight cells A3 and A4, then move the cursor to the lower right-hand corner of A4. When the black + appears, drag down until the small number to the right is 20. You have just used Quick Copy to generate a list of even numbers from 2 to 20 in column A. In B2, type the column heading y = 3x-5. You are now ready to insert a formula to calculate the corresponding y values for each value in column A. Enter the formula y=3x-5 in Excel format into B3, using the rules above. Calculate, by hand, the correct y value for x =2 and check it against the value that appears in B3. [Cell B3 should contain the formula =3*A3-5 and the output value 1.] Use Quick Copy to drag your formula down to obtain the y values that correspond with the x values in column A.

Answers:You've given all the instructions for doing this in Excel, but you haven't completed your question. It can't be answered as posted. "A chef has determined that the cost of preparing a certain menu item is calculated by multiplying the number o..."