Hey its 1:01 PM and as usual i'am not studying.
So today and yesterday summed up to have overall good outcomes. Over these 2 years of my studies in 11th and 12th standard gave me ups and downs. But the one thing i'am happy to carry along would be maturity, or maybe some fractions of it but still theirs presence, and its what matters.
Starting to an interesting topic, remember we all have studied matrices determinants vectors 3D all the algebra stuff, all turns out will get co-related in our further studies in mathematics as linear algebra. I'll tell you some awesome facts to which you can relate with your knowledge skills.
Remember those (second order) determinants we used to solve and get number out of it? Well, yes the number we got was actually the area of a parallelogram in 2D space lined up with basis vectors as forming the sides of parallelogram.
Some of you might have had a tough time with the row/ coulomb transformations to find out inverse or may be to solve determinant quicker. Well, yes those transformation actually meant squeezing or stretching the coordinate axis to transform the vectors.
More over mapping of vectors will be done by row/column matrix. say 1i+2j+3k would equals [1 2 3] as a coordinate or position vector.
All these were geometrical interpretation. For more you can check out the beautiful illustration with like the best possible animations in the series of illustrations by:
on the link:
https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
There are some beautiful topics to learn ahead, actually the things we've learned now will get scaled by a factor unimaginable for me now though.
*All the Physics like Mechanics, Electromagnetism in a comprehensive manner
*All Chemistry like Kinetics and all stuff again in a largely scaled manner
for more you can always google :)
Lastly,
Set realistic goals, try level best to achieve them, award yourself with some like free time for you tube, playing, ice cream or whatever but for 15 minutes not more than that then get back to work.
PEACE OUT!
08-04-2017
So today and yesterday summed up to have overall good outcomes. Over these 2 years of my studies in 11th and 12th standard gave me ups and downs. But the one thing i'am happy to carry along would be maturity, or maybe some fractions of it but still theirs presence, and its what matters.
Starting to an interesting topic, remember we all have studied matrices determinants vectors 3D all the algebra stuff, all turns out will get co-related in our further studies in mathematics as linear algebra. I'll tell you some awesome facts to which you can relate with your knowledge skills.
Remember those (second order) determinants we used to solve and get number out of it? Well, yes the number we got was actually the area of a parallelogram in 2D space lined up with basis vectors as forming the sides of parallelogram.
Some of you might have had a tough time with the row/ coulomb transformations to find out inverse or may be to solve determinant quicker. Well, yes those transformation actually meant squeezing or stretching the coordinate axis to transform the vectors.
More over mapping of vectors will be done by row/column matrix. say 1i+2j+3k would equals [1 2 3] as a coordinate or position vector.
All these were geometrical interpretation. For more you can check out the beautiful illustration with like the best possible animations in the series of illustrations by:
on the link:
https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
There are some beautiful topics to learn ahead, actually the things we've learned now will get scaled by a factor unimaginable for me now though.
*All the Physics like Mechanics, Electromagnetism in a comprehensive manner
*All Chemistry like Kinetics and all stuff again in a largely scaled manner
for more you can always google :)
Lastly,
Set realistic goals, try level best to achieve them, award yourself with some like free time for you tube, playing, ice cream or whatever but for 15 minutes not more than that then get back to work.
PEACE OUT!
08-04-2017
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