Tools

Linear Independence, Basis, Dimension and Co-ordinates

  1. On page 1, press “Click here for result” button given in Case 1, to check linear independence of S = ϕ 
  2. In Case 2, guess the answer by clicking the appropriate button for linear independence of S when 0 ∈ S.
  3. In Case 3 & 4, press “Click here for result” button to see the result and observe the geometry of the given case
  4. In Example 1a and Example 1b, press “Click here for result” button and observe the geometry and other details.
  5. In Example 2, enter the values of x1 , y1 and x2, y2. Then click on “Submit” button to see the geometry and other details.
  6. Click on the “Next” button to go to the next page.
  7. In the first block, press “Click here” buttons sequentially to understand the given examples.
  8. In the next block, 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. Press “Click here” in Step 1, “Step 2” and “Step 3” buttons one after the other to understand the process for verification.
  12. In Step 3 enter select the values u, v and w, x and click on “Submit” to check whether the chosen subset B of R2 is a basis or not.