<prompt> Hlalosa mohopolo oa linear algebra.nan  <response>: Instruction in English: Explain a concept of linear algebra. . Response in English: Linear algebra is a branch of mathematics dealing with linear equations, matrices and vector spaces. It deals with the study of lines, planes, and subspaces, and is concerned with the concepts of vector addition, scalar multiplication and linear transformations. One of the key concepts in linear algebra is that of vector spaces. A vector space is a collection of vectors that can be added together and multiplied by scalars to produce another vector in the collection. The most common example of a vector space is the three-dimensional Euclidean space, which is the set of all ordered triples x, y, z of real numbers. Another fundamental concept is that of linear transformations, which are functions that preserve the structure of a vector space. Linear transformations can be represented by matrices, which are rectangular arrays of numbers that can be used to transform one vector to another. One of the main goals of linear algebra is to understand the properties of matrices and how they can be used to solve systems of linear equations.Linear algebra plays a crucial role in many fields, including engineering, physics, and computer science, and is essential for those studying data science, machine learning and artificial intelligence. . Response in Sesotho: Linear algebra ke lekala la lipalo le sebetsanang le linear equations, matrices le vector spaces. E sebetsana le boithuto ba mela, lifofane, le li-subspaces, me e ameha ka maikutlo a ho eketsa li-vector, katiso ea scalar le liphetoho tsa mela. E ngoe ea mehopolo ea bohlokoa ho algebra ea linear ke ea libaka tsa vector. Sebaka sa vector ke pokello ea li-vector tse ka kenyelletsoang hammoho me tsa atisoa ke li-scalar ho hlahisa vector e ngoe pokellong. Mohlala o tlwaelehileng haholo wa sebaka sa vector ke sebaka sa Euclidean se mahlakore a mararo, e leng sete ya dinomoro tsa nnete tse hlophilweng ka makgetlo a mararo x, y, z. Khopolo e ngoe ea mantlha ke ea liphetoho tsa mela, e leng mesebetsi e bolokang sebopeho sa sebaka sa vector. Liphetoho tsa mela li ka emeloa ke matrices, e leng lipalo tse nang le khutlonnetsepa tse ka sebelisoang ho fetolela vector e ngoe ho ea ho e ngoe. E ngoe ea lipheo tsa mantlha tsa linear algebra ke ho utloisisa litšobotsi tsa matrices le hore na li ka sebelisoa joang ho rarolla litsamaiso tsa linear equations. Linear algebra e bapala karolo ea bohlokoa mafapheng a mangata, ho kenyeletsoa boenjiniere, fisiks, le mahlale a khomphutha, me e bohlokoa ho ba ithutang mahlale a data, ho ithuta ka mochini le bohlale ba maiketsetso. 