Question
MatrixInverse: The inverse of a matrix M to beanother matrix that
you can multiplyby Mand get the identity matrix.Physically the inverse of M
simply reverseswhatever Mdoes. If M stretches the y axis by a factor of 12then
its inverse compressesthe y axis by that same factor. If M rotates all vectors by
30° clockwisethen its inverse rotates all vectors by 30° counterclockwise.Not all
matrices can beinverted, however. In light of this discussion of what amatrix
does not have aninverse. To do this you should describe what transformationthis
Explanation / Answer
observe that the either the columns or rows of this matrixare ( 1,0,0), (0,0,0) ,(0,0,0). one is the standard basis vector and the others are zerovectors. we know that the zero vector is always linearlydependent. so, the rank of the matrix is less than the order of thematrix. or, the determinant of the matrix is zero. in other words it is a singular matrix. so, the corresponding linear transformation is singular. it is not invertible. on the other hand, the range of the linear transformation isspanned by ( 1,0,0). so, the subspace is a straight line. by reverting the straight line we get the same line and mergeswith itself. the linear transformation that determines this matrix is T(x,y,z) = ( x,0,0). try to follow the vectors to be columns as you are inpractice. but it is not a mistake to see a vector to be arow.