Area Of A Parallelogram Using Determinants - Linear Algebra Example Problems -

We use determinants to compute the area of a parallelogram in this example video. We also verify that the determinant approach to computing area yield the same answer obtained using "conventional" area computations.

While this particular example is for a 2-D parallelogram, the same concept applies to larger dimensions (e.g. 3-D parallelpipeds, etc.).

[pinkblack]

You basically saved my life. I actually got a pretty good grade on the exam by watching 50 of your videos starting 24 hours before the exam. Wow. Much better than the professor.

[huddybuddygreatness]

Thank you. Thank you so much

-Max, Denis, Hudson

[njallhalldorsson]

Excellent explanation Adam. I wonder how one should proceed if the corner of the parallelogram does not sit at the origin. Does this method work for such cases?

[hakeemnaa]

(5+7)(9+2)
= 5*9+5*2+7*9+7*2 ( four rectangles and you can draw it easily)

because T1=T3 and T2=T4
they can represent two rectangles R13+R24

so we have R13+R23+5*2+7*9 total areas

however what is in the video is
R13+R23+5*2+ (Parallelogram +5*2)


and of course
R13+R23+5*2+(7*9)
=R13+R23+5*2+ (Parallelogram +5*2)

[faizanulhaq]

y didnt u make videos for orthogonality :(

[neilsutherland]

Had no idea it was so simple. Thank you!

[papyrus]

Could I choose any two other vectors as well?

[serinacat]

like your vedio, you save my life, please post more vedio about linear algebra examples! please!!!

[WavyCats]

This video gave me serious insight into how to solve the area of a parallelogram at any time t when it is put through an affine transformation with respect to time t of the weighted average between initial and final images; however, it would help to show what happens when a corner is not at the origin.

[remi]

Thanks, appreciate the effort put into this :)