Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
4701	Evaluate	square root of 2(8- square root of 7)	$\sqrt{2} (8 - \sqrt{7})$
4702	Solve Using an Inverse Matrix	-x-4y-7z=-4 , x-7y-z=-7 , -x+6z=0	$- x - 4 y - 7 z = - 4$ , $x - 7 y - z = - 7$ , $- x + 6 z = 0$
4703	Evaluate	square root of 31500	$\sqrt{31500}$
4704	Solve Using an Inverse Matrix	(dx)/(dt)=y , (dy)/(dt)=-9.8sin(x)-0.5y	$\frac{d x}{d t} = y$ , $\frac{d y}{d t} = - 9.8 \sin (x) - 0.5 y$
4705	Evaluate	square root of 2115	$\sqrt{2115}$
4706	Evaluate	square root of 24502	$\sqrt{24 \cdot 50 \cdot 2}$
4707	Find the Rank	[[1,1,1],[a,b,c],[a^2,b^2,c^2]]=0	$[\begin{array}{c} 1 & 1 & 1 \\ a & b & c \\ a^{2} & b^{2} & c^{2} \end{array}] = 0$
4708	Find the Rank	[[1,1,2],[0,-1,-4],[0,0,1]]	$[\begin{array}{c} 1 & 1 & 2 \\ 0 & - 1 & - 4 \\ 0 & 0 & 1 \end{array}]$
4709	Find the Rank	[[1,-1,3],[6,7,-3],[9,4,6]]	$[\begin{array}{c} 1 & - 1 & 3 \\ 6 & 7 & - 3 \\ 9 & 4 & 6 \end{array}]$
4710	Find the Rank	[[1,2,-1]]	$[\begin{array}{c} 1 & 2 & - 1 \end{array}]$
4711	Find the Rank	[[1,2,-1],[-1,4,1],[0,6,0]]	$[\begin{array}{c} 1 & 2 & - 1 \\ - 1 & 4 & 1 \\ 0 & 6 & 0 \end{array}]$
4712	Find the Rank	[[1,2,3,4],[2,1,4,5],[1,5,5,7],[8,1,14,17]]	$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 2 & 1 & 4 & 5 \\ 1 & 5 & 5 & 7 \\ 8 & 1 & 14 & 17 \end{array}]$
4713	Find the Rank	[[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]]	$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \\ 13 & 14 & 15 & 16 \end{array}]$
4714	Find the Rank	[[1,2,3],[0,1,2],[2,5,8]]	$[\begin{array}{c} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 2 & 5 & 8 \end{array}]$
4715	Find the Rank	[[1,2,3],[4,5,6],[7,8,9]]	$[\begin{array}{c} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}]$
4716	Find the Rank	[[1,-3,1,0,-1],[1,-2,1,-1,0],[1,-1,1,-2,1]]	$[\begin{array}{c} 1 & - 3 & 1 & 0 & - 1 \\ 1 & - 2 & 1 & - 1 & 0 \\ 1 & - 1 & 1 & - 2 & 1 \end{array}]$
4717	Find the Rank	[[1,-4,2],[2,1,0],[5,-2,2]]	$[\begin{array}{c} 1 & - 4 & 2 \\ 2 & 1 & 0 \\ 5 & - 2 & 2 \end{array}]$
4718	Find the Rank	[[1,-4,2],[-2,8,-9],[-1,7,0]]	$[\begin{array}{c} 1 & - 4 & 2 \\ - 2 & 8 & - 9 \\ - 1 & 7 & 0 \end{array}]$
4719	Find the Rank	[[1,-7],[2,-10],[3,-13],[4,-16]]	$[\begin{array}{c} 1 & - 7 \\ 2 & - 10 \\ 3 & - 13 \\ 4 & - 16 \end{array}]$
4720	Find the Rank	[[1,h,4],[-5,10,-24]]	$[\begin{array}{c} 1 & h & 4 \\ - 5 & 10 & - 24 \end{array}]$
4721	Find the Rank	[[10,20,30,40]]	$[\begin{array}{c} 10 & 20 & 30 & 40 \end{array}]$
4722	Find the Rank	[[24],[-18]]=2y	$[\begin{array}{c} 24 \\ - 18 \end{array}] = 2 y$
4723	Find the Rank	[[3,0,2,2],[-6,42,24,54],[21,-21,0,-15]]	$[\begin{array}{c} 3 & 0 & 2 & 2 \\ - 6 & 42 & 24 & 54 \\ 21 & - 21 & 0 & - 15 \end{array}]$
4724	Find the Rank	[[3,1,0],[2,1,-4],[2,-1,20]]	$[\begin{array}{c} 3 & 1 & 0 \\ 2 & 1 & - 4 \\ 2 & - 1 & 20 \end{array}]$
4725	Find the Rank	[[-3,6,-1,1,-7],[1,-2,2,3,-1],[2,-4,5,8,-4]]	$[\begin{array}{c} - 3 & 6 & - 1 & 1 & - 7 \\ 1 & - 2 & 2 & 3 & - 1 \\ 2 & - 4 & 5 & 8 & - 4 \end{array}]$
4726	Find the Rank	[[3,x,-4],[4,2,1],[0,-4,5]]=6	$[\begin{array}{c} 3 & x & - 4 \\ 4 & 2 & 1 \\ 0 & - 4 & 5 \end{array}] = 6$
4727	Find the Rank	[[5,9,3],[3,5,6],[1,5,3]]	$[\begin{array}{c} 5 & 9 & 3 \\ 3 & 5 & 6 \\ 1 & 5 & 3 \end{array}]$
4728	Find the Rank	[[-6,2,-4],[9,-8,1],[-9,1,6]]	$[\begin{array}{c} - 6 & 2 & - 4 \\ 9 & - 8 & 1 \\ - 9 & 1 & 6 \end{array}]$
4729	Find the Rank	[[6,8,9],[3,5,7],[9,4,2]]	$[\begin{array}{c} 6 & 8 & 9 \\ 3 & 5 & 7 \\ 9 & 4 & 2 \end{array}]$
4730	Find the Rank	[[a-b,b+c],[-3d+c,2a-4d]]	$[\begin{array}{c} a - b & b + c \\ - 3 d + c & 2 a - 4 d \end{array}]$
4731	Find the Rank	[[i+1,2,1,-i],[1,i,2i,2]]	$[\begin{array}{c} i + 1 & 2 & 1 & - i \\ 1 & i & 2 i & 2 \end{array}]$
4732	Find the Rank	s=[[2,4,6,4],[2,5,7,6],[2,3,5,2]]	$s = [\begin{array}{c} 2 & 4 & 6 & 4 \\ 2 & 5 & 7 & 6 \\ 2 & 3 & 5 & 2 \end{array}]$
4733	Find the Rank	T[[a,b],[b,c]]	$T [\begin{array}{c} a & b \\ b & c \end{array}]$
4734	Find the Rank	[[1,-1,-3],[0,0,0]]	$[\begin{array}{c} 1 & - 1 & - 3 \\ 0 & 0 & 0 \end{array}]$
4735	Find the Rank	[[2,-1,-1,5],[-1,1,2,-3],[1,-2,3,4]]	$[\begin{array}{c} 2 & - 1 & - 1 & 5 \\ - 1 & 1 & 2 & - 3 \\ 1 & - 2 & 3 & 4 \end{array}]$
4736	Find the Rank	[[3,3],[3,3]]	$[\begin{array}{c} 3 & 3 \\ 3 & 3 \end{array}]$
4737	Find the Rank	[[-4,1],[5,6]]	$[\begin{array}{c} - 4 & 1 \\ 5 & 6 \end{array}]$
4738	Find the Nullity	[[1,-3,2,0],[-1,x,0,0],[0,-1,x,0],[0,0,-1,x]]=0	$[\begin{array}{c} 1 & - 3 & 2 & 0 \\ - 1 & x & 0 & 0 \\ 0 & - 1 & x & 0 \\ 0 & 0 & - 1 & x \end{array}] = 0$
4739	Find the Nullity	(2A^T)^-1=[[4,5],[3,4]]	${(2 A^{T})}^{- 1} = [\begin{array}{c} 4 & 5 \\ 3 & 4 \end{array}]$
4740	Find the Nullity	A=[[1,0,2,2,1],[0,2,4,0,-2],[5,-38,6,10,10],[5,-38,6,10,10],[-5,42,-6,-10,-7]]	$A = [\begin{array}{c} 1 & 0 & 2 & 2 & 1 \\ 0 & 2 & 4 & 0 & - 2 \\ 5 & - 38 & 6 & 10 & 10 \\ 5 & - 38 & 6 & 10 & 10 \\ - 5 & 42 & - 6 & - 10 & - 7 \end{array}]$
4741	Find the Nullity	f(t)=[[cos(2t)],[sin(t)]]	$f (t) = [\begin{array}{c} \cos (2 t) \\ \sin (t) \end{array}]$
4742	Find the Nullity	[[1,0.7,0.3,0],[-0.3,0.8,-0.5,0],[-0.15,-0.3,0.45,0]]	$[\begin{array}{c} 1 & 0.7 & 0.3 & 0 \\ - 0.3 & 0.8 & - 0.5 & 0 \\ - 0.15 & - 0.3 & 0.45 & 0 \end{array}]$
4743	Find the Nullity	[[1,0,2/9],[0,1,-4/9],[0,0,0]]	$[\begin{array}{c} 1 & 0 & \frac{2}{9} \\ 0 & 1 & - \frac{4}{9} \\ 0 & 0 & 0 \end{array}]$
4744	Find the Nullity	[[1,0,0,-3],[0,1,0,-1],[0,0,1,2]]	$[\begin{array}{c} 1 & 0 & 0 & - 3 \\ 0 & 1 & 0 & - 1 \\ 0 & 0 & 1 & 2 \end{array}]$
4745	Find the Norm	[[3,2,1],[5,3,2]]	$[\begin{array}{c} 3 & 2 & 1 \\ 5 & 3 & 2 \end{array}]$
4746	Find the Norm	[[-3,-2],[4,4],[5,7]]	$[\begin{array}{c} - 3 & - 2 \\ 4 & 4 \\ 5 & 7 \end{array}]$
4747	Find the Norm	[[3,-3,-6,-3],[2,-2,-4,h],[-2,3,-4,7]]	$[\begin{array}{c} 3 & - 3 & - 6 & - 3 \\ 2 & - 2 & - 4 & h \\ - 2 & 3 & - 4 & 7 \end{array}]$
4748	Find the Norm	[[3,9,8],[7,5,4],[1,5,6]]	$[\begin{array}{c} 3 & 9 & 8 \\ 7 & 5 & 4 \\ 1 & 5 & 6 \end{array}]$
4749	Find the Norm	[[4,1,-2,3],[1,1/4,-1/2,3/4],[2,1/2,-1,1]]	$[\begin{array}{c} 4 & 1 & - 2 & 3 \\ 1 & \frac{1}{4} & - \frac{1}{2} & \frac{3}{4} \\ 2 & \frac{1}{2} & - 1 & 1 \end{array}]$
4750	Find the Norm	[[4,5,0],[11,1,2],[1,5,2]]	$[\begin{array}{c} 4 & 5 & 0 \\ 11 & 1 & 2 \\ 1 & 5 & 2 \end{array}]$
4751	Find the Norm	[[4,5,-5,-3],[2,7,4,-3]]	$[\begin{array}{c} 4 & 5 & - 5 & - 3 \\ 2 & 7 & 4 & - 3 \end{array}]$
4752	Find the Norm	[[5,1,2,8,4,3,8,1],[5,9,1,5,7,2,9,1],[7,6,1,8,3,1,8,2],[0,5,0,8,5,4,6,7],[2,8,6,4,1,5,2,1],[0,0,0,0,0,0,0,0]]	$[\begin{array}{c} 5 & 1 & 2 & 8 & 4 & 3 & 8 & 1 \\ 5 & 9 & 1 & 5 & 7 & 2 & 9 & 1 \\ 7 & 6 & 1 & 8 & 3 & 1 & 8 & 2 \\ 0 & 5 & 0 & 8 & 5 & 4 & 6 & 7 \\ 2 & 8 & 6 & 4 & 1 & 5 & 2 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \end{array}]$
4753	Find the Norm	[[5,4,9],[-1,0,-1],[0,2,2],[-5,-4,-9]]	$[\begin{array}{c} 5 & 4 & 9 \\ - 1 & 0 & - 1 \\ 0 & 2 & 2 \\ - 5 & - 4 & - 9 \end{array}]$
4754	Find the Norm	[[7],[24]]	$[\begin{array}{c} 7 \\ 24 \end{array}]$
4755	Find the Norm	[[8],[-16],[11]]	$[\begin{array}{c} 8 \\ - 16 \\ 11 \end{array}]$
4756	Find the Norm	[[x,2,3,4,5,6],[y,-1,1,3,5,7]]	$[\begin{array}{c} x & 2 & 3 & 4 & 5 & 6 \\ y & - 1 & 1 & 3 & 5 & 7 \end{array}]$
4757	Find the Norm	u*(v[[i,j,k],[3,1,0],[2,0,4]])	$u \cdot (v [\begin{array}{c} i & j & k \\ 3 & 1 & 0 \\ 2 & 0 & 4 \end{array}])$
4758	Find the Norm	A=[[0.7,0.3],[0.6,0.4]]	$A = [\begin{array}{c} 0.7 & 0.3 \\ 0.6 & 0.4 \end{array}]$
4759	Find the Norm	[[0.4,1],[0.6,0]]	$[\begin{array}{c} 0.4 & 1 \\ 0.6 & 0 \end{array}]$
4760	Find the Norm	[[1,0],[6,-1]]	$[\begin{array}{c} 1 & 0 \\ 6 & - 1 \end{array}]$
4761	Find the Norm	[[1,-14,1,2,-2,-3],[2,-3,-1,-3,2,-1],[1,17,-4,1,1,-2],[-2,-52,-2,2,-1,-4],[3,24,-2,-1,1,3],[-1,-24,2,2,-1,-3]]	$[\begin{array}{c} 1 & - 14 & 1 & 2 & - 2 & - 3 \\ 2 & - 3 & - 1 & - 3 & 2 & - 1 \\ 1 & 17 & - 4 & 1 & 1 & - 2 \\ - 2 & - 52 & - 2 & 2 & - 1 & - 4 \\ 3 & 24 & - 2 & - 1 & 1 & 3 \\ - 1 & - 24 & 2 & 2 & - 1 & - 3 \end{array}]$
4762	Find the Norm	[[3,4,24],[7,1,31]]	$[\begin{array}{c} 3 & 4 & 24 \\ 7 & 1 & 31 \end{array}]$
4763	Find the Norm	[[5,10,15,20,25,30,35,40,45],[0,6,0,9,1,2,1,4,1,6,1,7,1,9,2,1,2,2]]	$[\begin{array}{c} 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 \\ 0 & 6 & 0 & 9 & 1 & 2 & 1 & 4 & 1 & 6 & 1 & 7 & 1 & 9 & 2 & 1 & 2 & 2 \end{array}]$
4764	Find the Norm	[[2.3,3.6],[1.4,5]]	$[\begin{array}{c} 2.3 & 3.6 \\ 1.4 & 5 \end{array}]$
4765	Find the Rank	(uxv)*w=[[a,b,d],[g,h,j],[k,l,n]]	$(u x v) \cdot w = [\begin{array}{c} a & b & d \\ g & h & j \\ k & l & n \end{array}]$
4766	Find the Rank	(2A^T)^-1=[[4,5],[3,4]]	${(2 A^{T})}^{- 1} = [\begin{array}{c} 4 & 5 \\ 3 & 4 \end{array}]$
4767	Find the Rank	A=[[1,-2,0,4],[3,1,1,0],[-1,-5,-1,8]]	$A = [\begin{array}{c} 1 & - 2 & 0 & 4 \\ 3 & 1 & 1 & 0 \\ - 1 & - 5 & - 1 & 8 \end{array}]$
4768	Find the Rank	A=[[i,-5,0],[1,i,-1]]	$A = [\begin{array}{c} i & - 5 & 0 \\ 1 & i & - 1 \end{array}]$
4769	Find the Rank	[[0,1,2],[3,4,5],[6,7,8]]	$[\begin{array}{c} 0 & 1 & 2 \\ 3 & 4 & 5 \\ 6 & 7 & 8 \end{array}]$
4770	Find the Rank	[[0,3,-2,0,6],[2,1,0,3,2],[0,-1,2,1,0],[1,0,0,-1,3],[1,3,-5,8,3]]	$[\begin{array}{c} 0 & 3 & - 2 & 0 & 6 \\ 2 & 1 & 0 & 3 & 2 \\ 0 & - 1 & 2 & 1 & 0 \\ 1 & 0 & 0 & - 1 & 3 \\ 1 & 3 & - 5 & 8 & 3 \end{array}]$
4771	Find the Rank	[[0,4,10,1],[4,8,18,7],[10,18,40,17],[1,7,17,3]]	$[\begin{array}{c} 0 & 4 & 10 & 1 \\ 4 & 8 & 18 & 7 \\ 10 & 18 & 40 & 17 \\ 1 & 7 & 17 & 3 \end{array}]$
4772	Find the Rank	[[0,1,2,3],[10,11,12,13],[20,21,22,23],[30,31,32,33]]	$[\begin{array}{c} 0 & 1 & 2 & 3 \\ 10 & 11 & 12 & 13 \\ 20 & 21 & 22 & 23 \\ 30 & 31 & 32 & 33 \end{array}]$
4773	Find the Rank	[[1,0,2/9],[0,1,-4/9],[0,0,0]]	$[\begin{array}{c} 1 & 0 & \frac{2}{9} \\ 0 & 1 & - \frac{4}{9} \\ 0 & 0 & 0 \end{array}]$
4774	Find the Rank	[[1,0,0],[0,1,0],[0,0,1]]*p	$[\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}] \cdot p$
4775	Find the Rank	[[1,0,1],[0,1,-1],[-1,0,1]]	$[\begin{array}{c} 1 & 0 & 1 \\ 0 & 1 & - 1 \\ - 1 & 0 & 1 \end{array}]$
4776	Find the Norm	-3A=[[-9,-1],[-2,-3]]	$- 3 A = [\begin{array}{c} - 9 & - 1 \\ - 2 & - 3 \end{array}]$
4777	Find the Norm	[[14/5],[2/5]]	$[\begin{array}{c} \frac{14}{5} \\ \frac{2}{5} \end{array}]$
4778	Find the Norm	[[0,0,0,-1],[0,1,-1,3],[0,0,1,2],[1,7,4,-4]]	$[\begin{array}{c} 0 & 0 & 0 & - 1 \\ 0 & 1 & - 1 & 3 \\ 0 & 0 & 1 & 2 \\ 1 & 7 & 4 & - 4 \end{array}]$
4779	Find the Norm	[[1,0,0,0,-8],[0,2,0,0,0],[-2,0,4,0,4],[0,-12,0,8,-8]]	$[\begin{array}{c} 1 & 0 & 0 & 0 & - 8 \\ 0 & 2 & 0 & 0 & 0 \\ - 2 & 0 & 4 & 0 & 4 \\ 0 & - 12 & 0 & 8 & - 8 \end{array}]$
4780	Find the Norm	[[1,1,1,0],[1,-2y,-4z,6],[-x,-y,-3z,6]]	$[\begin{array}{c} 1 & 1 & 1 & 0 \\ 1 & - 2 y & - 4 z & 6 \\ - x & - y & - 3 z & 6 \end{array}]$
4781	Find the Norm	[[1,-1,-1,-5],[-3,2,4,-1],[-10,10,11,12],[13,14,15,16]]	$[\begin{array}{c} 1 & - 1 & - 1 & - 5 \\ - 3 & 2 & 4 & - 1 \\ - 10 & 10 & 11 & 12 \\ 13 & 14 & 15 & 16 \end{array}]$
4782	Find the Norm	[[1,-1,2,3],[0,1,4,3],[1,0,3,5]]	$[\begin{array}{c} 1 & - 1 & 2 & 3 \\ 0 & 1 & 4 & 3 \\ 1 & 0 & 3 & 5 \end{array}]$
4783	Find the Norm	[[1,2,1],[1,2,1]]	$[\begin{array}{c} 1 & 2 & 1 \\ 1 & 2 & 1 \end{array}]$
4784	Find the Norm	[[1,-2,3],[0,1,-3]]	$[\begin{array}{c} 1 & - 2 & 3 \\ 0 & 1 & - 3 \end{array}]$
4785	Find the Norm	[[1,2,5,9],[11,14,19,5],[7,1,3,6],[13,17,21,0]]	$[\begin{array}{c} 1 & 2 & 5 & 9 \\ 11 & 14 & 19 & 5 \\ 7 & 1 & 3 & 6 \\ 13 & 17 & 21 & 0 \end{array}]$
4786	Find the Norm	[[1,2,-9,-8],[0,1,7,-3],[0,0,1,7]]	$[\begin{array}{c} 1 & 2 & - 9 & - 8 \\ 0 & 1 & 7 & - 3 \\ 0 & 0 & 1 & 7 \end{array}]$
4787	Find the Norm	[[1,-4,10],[0,0,0]]	$[\begin{array}{c} 1 & - 4 & 10 \\ 0 & 0 & 0 \end{array}]$
4788	Find the Norm	[[1+i],[1-i],[1]]	$[\begin{array}{c} 1 + i \\ 1 - i \\ 1 \end{array}]$
4789	Find the Norm	[[2,1],[-3,-1]]	$[\begin{array}{c} 2 & 1 \\ - 3 & - 1 \end{array}]$
4790	Find the Norm	[[2,2]]	$[\begin{array}{c} 2 & 2 \end{array}]$
4791	Find the Norm	[[2,6],[-4,-12]]	$[\begin{array}{c} 2 & 6 \\ - 4 & - 12 \end{array}]$
4792	Find the Norm	[[2,7],[3,11]]	$[\begin{array}{c} 2 & 7 \\ 3 & 11 \end{array}]$
4793	Find the Norm	[[-2],[2],[1]]	$[\begin{array}{c} - 2 \\ 2 \\ 1 \end{array}]$
4794	Find the Norm	[[223,333],[111,22]]	$[\begin{array}{c} 223 & 333 \\ 111 & 22 \end{array}]$
4795	Find the Null Space	x=1/(2[[5,4,8],[3,3,7]])	$x = \frac{1}{2 [\begin{array}{c} 5 & 4 & 8 \\ 3 & 3 & 7 \end{array}]}$
4796	Find the Null Space	x=[[5],[8],[3]]ax=0	$x = [\begin{array}{c} 5 \\ 8 \\ 3 \end{array}] a x = 0$
4797	Find the Null Space	[[ square root of 3,7,2,1],[5,9,15,8],[4,6,7,6]]	$[\begin{array}{c} \sqrt{3} & 7 & 2 & 1 \\ 5 & 9 & 15 & 8 \\ 4 & 6 & 7 & 6 \end{array}]$
4798	Find the Null Space	[[12],[3],[-9]]	$[\begin{array}{c} 12 \\ 3 \\ - 9 \end{array}]$
4799	Find the Null Space	[[1,6,5,-7],[0,1,2,-1],[0,0,1,2]]	$[\begin{array}{c} 1 & 6 & 5 & - 7 \\ 0 & 1 & 2 & - 1 \\ 0 & 0 & 1 & 2 \end{array}]$
4800	Find the Null Space	[[1,7,0,6,0],[0,0,1,9,0],[0,0,0,0,8]]	$[\begin{array}{c} 1 & 7 & 0 & 6 & 0 \\ 0 & 0 & 1 & 9 & 0 \\ 0 & 0 & 0 & 0 & 8 \end{array}]$