The image is the set of all points in $\mathbb{R}^4$ that you get by multiplying this matrix to points in $\mathbb{R}^5$, you can find these by checking the matrix on the standard basis. The kernel is the set of all points in $\mathbb{R}^5$ such that, multiplying this matrix with them gives the zero vector.
These seven companies alone have produced almost one-fifth (18.7 percent) of all industrial carbon released into the atmosphere since the dawn of the Industrial Revolution.
With a goal of reducing carbon fiber production costs by 50 percent, the Energy Departmentâs new Carbon Fiber Technology Facility at Oak Ridge National Laboratory is working with manufacturers and researchers to develop better and cheaper processes for producing carbon fibers.ith a goal of reducing carbon fiber production costs by 50 percent, the Energy Departmentâs new Carbon Fiber Technology Facility at Oak Ridge National Laboratory is working with manufacturers and researchers to develop better and cheaper processes for producing carbon fibers.