linear algebra

Feb 3rd, 2012
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Corresponding to matrix there is a linear transformation , what is the transformation and this transformation goes from what space to what space Consider the system of equations

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(1)Consider the system of equations Where So, (2)Corresponding to matrix there is a linear transformation , what is the transformation and this transformation goes from what space to what spaceIf be a linear transformation and and be basis for and then in order to write down the matrix of relative to the basis and So this transformation goes to one-to-one correspondence between linear transformations and matrices.Hence (3)What is the determinant for matrix A and what does this tell you about matrix A being invertible or notDeterminant of a square matrix:A square matrix having same number of rows and columns it will have array of numbers. These numbers also determine a determinant having rows and columns and is denoted by If , we have Hence is invertible.Hence the determinant for matrix A and what does this tell you about matrix A being invertible or notZero.(4)What is a basis for the Null Space of , what is the rank of the Null Space and what does this tell you about the linear transformation being one-to-one.Consider the matrix by Gaussian-Jordan elimination and the null space of is the set of such that and reduce matrix and the equation with zero on the R.H.S Let be an matrix , the nullspace of the matrix denoted and all dimensional column vectors such that So,is the number of all columns in the matrix So this transformation goes to one-to-one correspondence between linear transformations and matrices.Rank of null Space is That imp

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