Tools

Linear Independence, Basis, Dimension and Co-ordinates

  1. On the first page, four cases are provided to study linear independence of various subsets of R2.
  2. In each case, guess the answer by clicking the appropriate button. It will display correctness of the answer together with the reason.
  3. On the same page, in Example 1a and Example 1b, observe the geometry and press “Click here for reason” button to see the reason for the given statement.
  4. In Example 2, enter the values of x1 , y1 and x2, y2. Then click on “Submit” button to see the geometry and other details.
  5. Click on the “Next” button to go to the next page.
  6. In the first block, press “Click here” button to understand the given examples.
  7. In the next block, hands on practice is provided to construct a basis of R2.
  8. In the first section, select the values of x, y to choose first element a of basis and click the “Geometry” button to observe the chosen point on the graph.
  9. Now select the values of x1, y1 to choose b and click on “Geometry” button to observe both the points a and b together on the graph.
  10. Observe the basis thus constructed in the 3rd section of the block.
  11. Next block provides a stepwise process to check whether a given nonempty subset B of R2 is a basis or not.
  12. Press “Click here” in Step 1, “Step 2” and “Step 3” buttons one after the other to understand the process for verification.
  13. In Step 3, hands on practice is also provided. To choose a subset B of R2, select the values u, v and w, x and click on “Submit” to check whether the chosen subset B is a basis or not.