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![]() (ii) The transaction involves an exchange or transfer of money or money’s worth such as goods or services. (i) There must be at least two parties to a transaction. In short the following three points are worth noting about business transactions: One party receives the benefit which the other party gives. The purchase and sale of goods for cash or on credit, the receipts and payments of cash etc., are termed as business transactions since these activities involve exchange of values between parties.Ī business transaction therefore results in some property, goods or services changing hands. A business transaction is a business activity involving the exchange of money and goods or services for money or for a right to collect money between accounting entities – person (natural and artificial) and which can be objectively measured. ![]() A supplier invoice also supports the recordation of an expense, inventory item, or fixed asset.Accounting Process is primarily concerned with the business transactions. Supplier invoice: This is also a source document that supports the issuance of a cash, cheque or electronic payment to a supplier.Sales order: This document, when coupled with a bill of lading and packing list, can be used to invoice a customer, which in turn generates a sale transaction.Packing slip: This describes the items shipped to a customer, and so supports the recordation of a sale transaction.Credit card receipt: This can be used as evidence for a disbursement of funds from petty cash.Bank statement: It contains a number of adjustments to a company’s balance of cash on hand that the company should reference to bring its records into alignment with those of the bank.Question: Give examples of various source documents which are used by an accountant to record a business transaction.Īnswer: Some of the source documents which help in the preparation of financial accounts, are as follows: It can also be in electronic form, such as an electronic record of the hours worked by an employee, as entered into a company’s timekeeping system. Many source documents are also stamped by personnel, to indicate an approval, or on which to write down the current date or the accounts to be used to record the transaction. A source document does not necessarily have to be a paper document. A Quantitative field (number of hours, the quantity of goods etc).A description of a business transaction. ![]() ![]() They usually contain the following information: This is where the role of source documents fall into place. Usually, auditors later review a company’s financial statements and need to verify that transactions have, in fact, occurred. Source documents are typically retained for use as a medium of evidence. Source documents in accounting terms are the physical basis or documents based on which business transactions are recorded.
![]() PSE Fire-Flite Elite Series Graphite Bow with Vector WheelsOriginal ownerRH 30” Draw 55-70#FastFlight StringIncludes PSE Mongoose 106 5-pin guarded sightStabilizer and extensionHydralizer StabilizerArrow launcher rest and peepAccessories Included. Archery Set PSE Fire-Flite Elite Series Bow with Vector Wheels - $400 (Canandaigua, NY).PSE Fire-flite express compound bow with quiver, right-handed. PSE Fire-Flite Express Compound Bow - $150 (New Cambria).Bowjax string vibration dampeners as well. It also has a neon green and black custom bow string. It has Hushpuk limb and riser vibration dampeners mounted on it. It has a Trophy Taker Smack Down drip away arrow rest. ![]() PSE Fire-Flite 33 compound bow - $150 (Horseheads)įor sale: PSE Fire-Flite 33 compound bow.Also have a field box with extra target heads. Include hard plastic case, quiver with 8 hunting arrows, quick release, sights, extra arrow box with some new arrows most are for target use. In excellent condition don't use it anymore. PSE Fire Flite 33 Compound Bow - $150 (Kure Beach).Feel free to make me a reasonable offer.Can mee. PSE Fire-Flite 33 Compound Bow - $150 (Lancaster)įor sale is a PSE Fire-Flite 33 Compound Bow in very nice condition in Seclusion 3D camo pattern.The bow is setup at 29" pull length and 70 #.The bow includes a rest, matching quiver, NAP Shockblocker stabilizer, and a Cabela's release.PSE Fire-Flite Elite Series Graphite Bow with Vector WheelsOriginal ownerRH 30” Draw 55-70#FastFlight StringIncludes PSE Mongoose 106 5-pin guarded sightStabilizer and extensionHydralizer StabilizerArrow launcher rest and peepAccessories Included:Bus. Archery Set PSE Fire-Flite Elite Series Bow w/Vector Wheels - $375 (Canandaigua, NY). In this section, we discuss the non-singularity of the NSZ-matrix. A Necessary and Sufficient Condition for Non-Singularity of the Z-Matrix Whose Row Sums Are All Non-Negative is itself.īased on the above, we confirm the following basic proposition.Ģ. Similarly, refers to a submatrix of whose row elements belong to and column elements belong to, and refers to a submatrix of whose row and column elements belong to. refers to a submatrix of whose row elements belong to and column elements belong to. When is a proper subset, we define as the complement of. refers to a submatrix of whose row and column elements belong to. Let be a set of number of rows and columns of a square matrix and let be a subset of which is not empty. Here, we define the notation for submatrices in this paper. Theorem 1.7 Similar matrices have the same eigenvalue 6. Theorem 1.6 When two matrices are similar, if one matrix is non-singular, the other is also non-singular. If holds for the square matrices and and a non-singular matrix, and are called similar to each other. The determinant of a matrix whose column vectors are linearly dependent is zero 5. Theorem 1.5 If the row sums of a square matrix are all zeroes. Regarding the inverse of an M-matrix, is satisfied 4. However, as it receives less attention that diagonal elements of are or more, we confirm this aspect. As Theorems 1.3 and 1.4 are well known, we entrust the proof to another work 3. In particular, all diagonal elements of the inverse are equal to or more than 2. In this case, and all elements of the inverse of an M-matrix are non-negative. Theorem 1.4 An M-matrix is non-singular if and only if. If a Z-matrix satisfies, is called an M-matrix 1. ![]() Then there exists a non-negative eigenvector corresponding to. Let be the maximum non-negative eigenvalue of. Theorem 1.3 A non-negative square matrix always has a non-negative eigenvalue. On the other hand, the diagonal elements of B are. Take a real number which is equal to or more than all diagonal elements and construct the matrix where refers to the unit matrix. ![]() The determinant of a square matrix is denoted in this paper. We first state the basic propositions of linear algebra used in this paper. However, we will prove the latter condition first, and then address the former condition. Therefore, if we can find a necessary and sufficient condition for non-singularity of the NPZ-matrix, we find the necessary and sufficient condition for non-singularity of the NSZ-matrix automatically. Thus,Īs Theorem 1.1 shows, the NSZ-matrix is a type of the NPZ-matrix. If we divide both sides of by, we obtain for. Hence, for is satisfied.Ĭonversely, consider that is an NPZ-matrix which satisfies for where. If is an NSZ-matrix, the ith element of is. Let be a set of numbers, and be a positive vector with all elements equal to the same number. Theorem 1.1 An NSZ-matrix is equivalent to an NPZ-matrix where all elements of are the same number. The following relation exists between these matrices. In this paper, we denote this as a Non-negative Product Z-matrix (NPZ-matrix). The second is the Z-matrix A which satisfies where. In this paper, we denote this as a Non-negative Sums Z-matrix (NSZ-matrix). The first is the Z-matrix whose row sums are all non-negative. The purpose of this paper is to show a necessary and sufficient condition for non-singularity of two types of Z-matrices. Keywords:Z-Matrix, M-Matrix, Non-Negative Matrix, Diagonal DominanceĪ real square matrix whose non-diagonal elements are non-positive is called a Z-matrix. ![]() In this paper, we present a different proof and show that these conditions can be also derived from theirs. Robert Beauwens and Michael Neumann previously presented conditions similar to these conditions. The non-singularity condition for this matrix is such that or such that for. ![]() Let be a subset of which is not empty, and be the complement of if is a proper subset. Let be the ith row and the jth column element of, and be the jth element of. The second is for the Z-matrix which satisfies where. The non-singularity condition for this matrix is that at least one positive row sum exists in any principal submatrix of the matrix. The first is for the Z-matrix whose row sums are all non-negative. This paper shows a necessary and sufficient condition for non-singularity of two types of Z-matrices. Received 23 April 2014 revised accepted Ī real square matrix whose non-diagonal elements are non-positive is called a Z-matrix. This work is licensed under the Creative Commons Attribution International License (CC BY). Email: © 2014 by author and Scientific Research Publishing Inc. ![]() So, how much is Mel Blanc worth at the age of 81 years old? Mel Blanc’s income source is mostly from being a successful Actor. His net worth has been growing significantly in 2022-2023. ![]() He is a member of famous Actor with the age 81 years old group. We recommend you to check the complete list of Famous People born on 30 May. At the time of his death, he was estimated to have a net worth of $10 million. He was posthumously inducted into the National Radio Hall of Fame in 1994. He was also a regular on the Jack Benny radio show, and appeared in several films.īlanc died on July 10, 1989, at the age of 81. This interview took place in October 2011, on the Channel-6 Good Day Big Bear Show The Blanc’s Big Bear home sits in Sawmill Cove. He was also a prolific singer, recording hundreds of songs for various cartoon characters. Historical Videos Noel Blanc, Kim Sweet and Rick Keppler discuss Noel & Katherine Blanc’s home at Big Bear Lake. He carries on his father's legacy of personal appearances, notably in the booth as a celebrity guest for the 20 Chevrolet Monte Carlo 400 NASCAR Races featuring the Looney Tunes characters in themed paint schemes for Chevrolet drivers. He was the first voice actor to receive a star on the Hollywood Walk of Fame.īlanc's career spanned more than six decades, and he voiced thousands of characters. The Noel dress is cut from a beautifully draped stretch jersey and features a plunge, halter neckline and body con midi length skirt with a thigh high split. Noel Blanc is CEO of Warner-Blanc, a joint venture of Warner Bros. Oh quand j'entend chanter Noel J'aime a revoir mes joies d'enfant Le sapin scintillant, la neige d'argent Noel, mon beau Noel blanc Oh when I hear singing Christmas I like to see again the joys of my childhood The scintillating fir, the silver snow Christmas, my beautiful Christmas Oh quand j'entends sonner au ciel L'heure ou le bon vieillard. He began his career in radio in the 1930s, and by the 1940s had become one of the most sought-after voice actors in the business. Cartoons, where he voiced characters such as Bugs Bunny, Daffy Duck, Porky Pig, Tweety Bird, Sylvester the Cat, Yosemite Sam, Foghorn Leghorn, Marvin the Martian, Pepé Le Pew, Speedy Gonzales, the Tasmanian Devil, and many others.īlanc was born in San Francisco, California, on May 30, 1908. He is best known for his work with Warner Bros. Mel Blanc was an American voice actor, comedian, singer, and radio personality. |
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