Subtraction and addition

Addition or subtraction of matrices is done element-wise and thus is straightforward. Obviously, the dimensions of the matrices to be added have to match. 

In Matlab the standard mathematical operators for addition (+) and subtraction (-) can be used directly with matrices. As with transposition, Matlab automatically calls the appropriate functions to perform the operations.  

Note that Matlab directly adds/subtracts a single scalar element-wise to/from matrices. Suppose you want to subtract element foi,2 (a scalar) from all elements of matrix A. A valid Matlab command would be  

In Excel, mathematical operations of one or more cells can be dragged to other cells. Since a cell represents one element of an array or matrix, the effect will be an element-wise matrix calculation. Thus, addition and subtraction of matrices are straightforward. An example  

Cells A3 C4 and E3 G4 comprise the elements of array A and B respectively. First, in cell 13, the addition is done for one pair of elements, A3+E3 (ai,i+bi,i). Then, the calculation is repeated by dragging cell 13 to the remaining cells of the rectangle I3 K4. 

To add or subtract numbers in exponential or scientific notation, both numbers must have the same power of ten. If they don t, you must convert them to the same power. Here s an addition example  

To multiply numbers expressed in exponential notation, multipiy the coefficients (the numbers) and add the exponents (powers of ten)  

To divide numbers expressed in exponential notation, divide the coefficients and subtract the exponent of the denominator from the exponent of the numerator  

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Separate driver and receiver and front balancing. The board can be programmed to use absolute probes, differential probes, additive and subtractive fluxes it can be operated in three modes receiver only, driver only, and driver-receiver. All of these configurations only depend on the way the probe is connected, and software configuration. Each board has connections for 2 drivers and 2 receivers. 

To estimate the computational time required in a Gaussian elimination procedure we need to evaluate the number of arithmetic operations during the forward reduction and back substitution processes. Obviously multiplication and division take much longer time than addition and subtraction and hence the total time required for the latter operations, especially in large systems of equations, is relatively small and can be ignored. Let us consider a system of simultaneous algebraic equations, the representative calculation for forward reduction at stage is expressed as... 

Addition and subtraction of matrices is canied out by adding or subtracting coiTcsponding elements. With matrices denoted by boldface capital letters and matrix elements by lower case letters, if... 

As a general rule, mathematical operations involving addition and subtraction are carried out to the last digit that is significant for all numbers included in the calculation. Thus, the sum of 135.621, 0.33, and 21.2163 is 157.17 since the last digit that is significant for all three numbers is in the hundredth s place. 

Addition and Subtraction Only like terms can be added or sub-trac ted in two algebraic expressions. 

Addition and Subtraction The operations of addition (-h) and subtraction (—) of two or more matrices are possible if and only if they have the same number of rows and columns. Thus A B = (ay by) i.e., addition and subtraction are of corresponding elements. 

Matrix algebra also involves the addition and subtraction of matrices. The rules for this are as follows ... 

Multiplication, division, addition, and subtraction can be carried out directly on your calculator. Try the following exercises ... 

Addition and subtraction When adding or subtracting, make sure that the number of decimal places in the result is the same as the smallest number of decimal places in the data. For example, 0.10 g + 0.024 g = 0.12 g. 

The simplest bonding model requires only the addition of wave functions. Later in this chapter, we show that a complete description of bonding often requires both addition and subtraction of wave functions. 

The next step in the deveiopment of moiecuiar orbitai theory is to consider the MOs formed by additive and subtractive overiap of atomic p orbitais. We use moiecuiar oxygen as a case study. 

Additive and subtractive combinations of p orbitals lead to bonding and antibonding orbitals, (a) End-on overlap gives a orbitals, (b) Side-by-side overlap gives orbitals. 

The isotopic molar masses are precise to five or more significant figures, so we are tempted to express the result with five significant figures. The mass defect is determined by addition and subtraction, however, and two of the isotopic molar masses are known to just three decimal places, so the mass defect is precise to three decimal places, and the... 

Although blocks are used to identify many types of mathematical operations, operations of addition and subtraction are represented by a circle, called a summing point. As shown in Figure 6, a summing point may have one or several inputs. Each input has its own appropriate plus or minus sign. A summing point has only one output and is equal to the algebraic sum of the inputs. 

These are solved by matrix manipulations. Programs are in POLYMATH, CONSTANTINIDES AND CHAPRA CANALE. When the number of equations is not large, a manual procedure can be used to eliminate one variable at a time by reduction of the leading coefficients to unity and appropriate additions and subtractions of the equations. 

Of the multitude of ID 13C NMR experiments that can be performed, the two most common experiments are a simple broadband proton-decoupled 13C reference spectrum, and a distortionless enhancement polarization transfer (DEPT) sequence of experiments [29]. The latter, through addition and subtraction of data subsets, allows the presentation of the data as a series of edited experiments containing only methine, methylene and methyl resonances as separate subspectra. Quaternary carbons are excluded in the DEPT experiment and can only be observed in the 13C reference spectrum or by using another editing sequence such as APT [30]. The individual DEPT subspectra for CH, CH2 and CH3 resonances of santonin (4) are presented in Fig. 10.9. 

Addition and subtraction the answer should have the same number of decimal places as the quantity with the fewest number of decimal places. 

For addition and subtraction problems, round the answer off to the same number of decimal points as the measurement with the fewest decimal places. 

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