If {0} is the only linearly dependent set of V then the dimension of V is???

[@maheshgawande1833]

Thank you sir, Please make such video's, based on what they asked in interview

[@DrMathaholic]

Welcome Mahesh.

[@stewartgarikayi4560]

Hello Sir ... today I have a question.May you help me 😊

[@stewartgarikayi4560]

Rotate using matrix methods and translate the coordinate axes of the curve -7x²+24xy+7y²-10x+20y+1=0 to standard position, identify the conic and find the angle of rotation.[10].

[@stewartgarikayi4560]

Help please

[@stewartgarikayi4560]

A question again Sir. Prove that for any subspace S of V ,S + S= S

[@DrMathaholic]

Let x belongs to S+S then x = y+z for some y belongs to first S and z belongs to second S. But y and z are in S and S being a subspace, y+z is again in S. So x is in S. Thus S+S subset of S. On the other hand, Let x belongs to S, then x can be written as x=x+0, where x belongs to x and 0 belongs to second S. Thus , x=x+0 belongs to S+S. Hence S subset of S+S. Hence both are equal.

[@stewartgarikayi4560]

@@DrMathaholic Thank you Sir

[@stewartgarikayi4560]

Let P 3 be the vector space of all polynomials of degree 3 and less ,with real coefficients with the basis {1,t,t,t²,t³} .T:P3-->P3 is a linear transformation such that T(1)= 1 + t². T(t)=t, T(t²)=2 + 3t², T(t³)= 1-2t +t³ . Compute T(3-6t+2t²-5t³)

[@stewartgarikayi4560]

Help

[@DrMathaholic]

@stewartgarikayi4560 T(3-6t+2t^2-5t^3)= 3T(1)-6T(t)+2T(t^2)-5T(t^3)... reason being, T is a Linear transformation.. Now substitute the values of T(1), T(t), T(t^2), and T(t^3) to get the answer. Let me know in case more details required

[@stewartgarikayi4560]

Thank you Sir .Well explained 😊

[@DrMathaholic]

@@stewartgarikayi4560 welcome...

[@stewartgarikayi4560]

hello Sir I have a question . {(x,y,z): xyz=0} determine if it forms a subspace

[@DrMathaholic]

Nope..it do not form a subspace . Take (1,0,1) and (0,1,0). Both these vectors are in the given set as product of components is zero but their addition is (1,1,1) which is not in the given set as the product of components is non zero

[@stewartgarikayi4560]

Thank you 🎉

[@DrMathaholic]

@@stewartgarikayi4560 welcome

[@stewartgarikayi4560]

I wish to join your WhatsApp groups for more learning. Your teaching is awesome

[@DrMathaholic]

@@stewartgarikayi4560 I have not created any groups.. It's just here.. You can see the videos n ask your doubts. I will try my best to solve them.. 😊