2016 SN P1 ALGEBRA - WebCampus
... to eliminate the x1 terms from all the equations below it. To do this, add proper multiples of the first equation to each of the succeeding equations. Then, disregard the first equation and eliminate the next variable - usually x2 - from the last m−1 equations just as before, that is, by adding prop ...
... to eliminate the x1 terms from all the equations below it. To do this, add proper multiples of the first equation to each of the succeeding equations. Then, disregard the first equation and eliminate the next variable - usually x2 - from the last m−1 equations just as before, that is, by adding prop ...
Matrix Arithmetic
... multiplying, and dividing(when possible) real numbers. So how can we add and subtract two matrices? Eventually we will multiply matrices, but for now we consider another multiplication. Here are the definitions. Definition 2 Let A = (aij ) and B = (bij ) be m × n matrices. We define their sum, denot ...
... multiplying, and dividing(when possible) real numbers. So how can we add and subtract two matrices? Eventually we will multiply matrices, but for now we consider another multiplication. Here are the definitions. Definition 2 Let A = (aij ) and B = (bij ) be m × n matrices. We define their sum, denot ...
Matrix algebra for beginners, Part II linear transformations
... Vectors arise in physics as mathematical representations of quantities like force and velocity which have both magnitude and direction. If we fix a point as the origin , then the collection of vectors which originate from this point form a vector space . To have something concrete in mind, we can th ...
... Vectors arise in physics as mathematical representations of quantities like force and velocity which have both magnitude and direction. If we fix a point as the origin , then the collection of vectors which originate from this point form a vector space . To have something concrete in mind, we can th ...
A set of equations of the form (1) a11x1 + a12x2 + ··· + a 1nxn = c1
... are, respectively, 1 by n column vector and 1 by m column vector. By a solution of (1) we mean an n-vector (x1 , . . . , xn ) for which all the equations in (1) are satisfied simultaneously. The solution set of (1) consists of all such n-vectors; it is a subset of Vn , naturally. Theory of systems o ...
... are, respectively, 1 by n column vector and 1 by m column vector. By a solution of (1) we mean an n-vector (x1 , . . . , xn ) for which all the equations in (1) are satisfied simultaneously. The solution set of (1) consists of all such n-vectors; it is a subset of Vn , naturally. Theory of systems o ...
3.4 Solving Matrix Equations with Inverses
... The matrix A is called the coefficient matrix and it entries are the coefficients on the variables when they are written in the same order in each equation. The matrix X is called the variable matrix and contains the two variables in the problem. The matrix B is called the constant matrix and contai ...
... The matrix A is called the coefficient matrix and it entries are the coefficients on the variables when they are written in the same order in each equation. The matrix X is called the variable matrix and contains the two variables in the problem. The matrix B is called the constant matrix and contai ...
