Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
4601	Find the Kernel	[[1,1,0,2,-3],[0,0,1,-5,4],[0,0,0,0,0]]=[[0],[1],[0]]	$[\begin{array}{c} 1 & 1 & 0 & 2 & - 3 \\ 0 & 0 & 1 & - 5 & 4 \\ 0 & 0 & 0 & 0 & 0 \end{array}] = [\begin{array}{c} 0 \\ 1 \\ 0 \end{array}]$
4602	Find the Kernel	[[1,1,1,1],[3,2,-1,2],[2,2,1,-1],[-1,3,2,-1]]=[[0],[7],[5],[2]]	$[\begin{array}{c} 1 & 1 & 1 & 1 \\ 3 & 2 & - 1 & 2 \\ 2 & 2 & 1 & - 1 \\ - 1 & 3 & 2 & - 1 \end{array}] = [\begin{array}{c} 0 \\ 7 \\ 5 \\ 2 \end{array}]$
4603	Find the Kernel	[[1,2,3,4],[0,0,1,2],[0,0,0,0]]=[[0],[0],[0]]	$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 \end{array}] = [\begin{array}{c} 0 \\ 0 \\ 0 \end{array}]$
4604	Find the Kernel	[[3,1],[4,1]]x=[[5,-1],[2,3]]	$[\begin{array}{c} 3 & 1 \\ 4 & 1 \end{array}] x = [\begin{array}{c} 5 & - 1 \\ 2 & 3 \end{array}]$
4605	Find the Kernel	[[3],[1],[-2]]=[[1],[2],[5]]	$[\begin{array}{c} 3 \\ 1 \\ - 2 \end{array}] = [\begin{array}{c} 1 \\ 2 \\ 5 \end{array}]$
4606	Find the Kernel	[[6,-2,-4,4],[3,-3,-6,1],[-12,8,21,-8],[-6,0,-10,7]][[x],[y],[z],[w]]=[[2],[-4],[8],[-43]]	$[\begin{array}{c} 6 & - 2 & - 4 & 4 \\ 3 & - 3 & - 6 & 1 \\ - 12 & 8 & 21 & - 8 \\ - 6 & 0 & - 10 & 7 \end{array}] [\begin{array}{c} x \\ y \\ z \\ w \end{array}] = [\begin{array}{c} 2 \\ - 4 \\ 8 \\ - 43 \end{array}]$
4607	Find the Kernel	[[9,-36,30],[-36,192,-180],[30,-180,180]][[x],[y],[z]]=[[15],[-48],[30]]	$[\begin{array}{c} 9 & - 36 & 30 \\ - 36 & 192 & - 180 \\ 30 & - 180 & 180 \end{array}] [\begin{array}{c} x \\ y \\ z \end{array}] = [\begin{array}{c} 15 \\ - 48 \\ 30 \end{array}]$
4608	Find the Kernel	[[a,b],[c,d]]*[[4],[1]]=[[0],[0]]	$[\begin{array}{c} a & b \\ c & d \end{array}] \cdot [\begin{array}{c} 4 \\ 1 \end{array}] = [\begin{array}{c} 0 \\ 0 \end{array}]$
4609	Find the Kernel	[[d+j^t,g+k^t,h+l^t],[d+j,g+k,h+l],[n,o,p]]=(1-t^2)[[d,g,h],[j,k,l],[n,o,p]]	$[\begin{array}{c} d + j^{t} & g + k^{t} & h + l^{t} \\ d + j & g + k & h + l \\ n & o & p \end{array}] = (1 - t^{2}) [\begin{array}{c} d & g & h \\ j & k & l \\ n & o & p \end{array}]$
4610	Find the Kernel	S([[a],[b],[c]])=[[a+3b-6c],[2a+b+c],[a+5b+c]]	$S ([\begin{array}{c} a \\ b \\ c \end{array}]) = [\begin{array}{c} a + 3 b - 6 c \\ 2 a + b + c \\ a + 5 b + c \end{array}]$
4611	Determine if Linear	[[2,-4,6],[1,-3,5],[3,-7,12]]x=[[14],[7],[2]]	$[\begin{array}{c} 2 & - 4 & 6 \\ 1 & - 3 & 5 \\ 3 & - 7 & 12 \end{array}] x = [\begin{array}{c} 14 \\ 7 \\ 2 \end{array}]$
4612	Determine if Linear	[[4,-3],[3,1]][[x],[y]]=[[-3],[4]]	$[\begin{array}{c} 4 & - 3 \\ 3 & 1 \end{array}] [\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} - 3 \\ 4 \end{array}]$
4613	Determine if Linear	[[5,-3,12],[2,3,9]][[x],[y],[z]]=[[26],[2]]	$[\begin{array}{c} 5 & - 3 & 12 \\ 2 & 3 & 9 \end{array}] [\begin{array}{c} x \\ y \\ z \end{array}] = [\begin{array}{c} 26 \\ 2 \end{array}]$
4614	Determine if Linear	[[7],[2],[5]]u+[[2],[-4],[8]]v+[[5],[2],[8]]w=[[35],[-18],[102]]	$[\begin{array}{c} 7 \\ 2 \\ 5 \end{array}] u + [\begin{array}{c} 2 \\ - 4 \\ 8 \end{array}] v + [\begin{array}{c} 5 \\ 2 \\ 8 \end{array}] w = [\begin{array}{c} 35 \\ - 18 \\ 102 \end{array}]$
4615	Determine if Linear	[[x],[y]]=[[0],[x]]	$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 0 \\ x \end{array}]$
4616	Find the Nullity	[[1,1,-2,0,1,-3],[1,2,-3,0,-3,-2],[1,3,-4,0,-4,5],[1,3,-3,1,0,-3],[1,4,-5,0,-8,14]]	$[\begin{array}{c} 1 & 1 & - 2 & 0 & 1 & - 3 \\ 1 & 2 & - 3 & 0 & - 3 & - 2 \\ 1 & 3 & - 4 & 0 & - 4 & 5 \\ 1 & 3 & - 3 & 1 & 0 & - 3 \\ 1 & 4 & - 5 & 0 & - 8 & 14 \end{array}]$
4617	Find the Nullity	[[1,-1,-2],[-1,-1,-3+k]]	$[\begin{array}{c} 1 & - 1 & - 2 \\ - 1 & - 1 & - 3 + k \end{array}]$
4618	Find the Nullity	[[1,4,0,3,0],[0,0,1,-5,0],[0,0,0,0,4]]	$[\begin{array}{c} 1 & 4 & 0 & 3 & 0 \\ 0 & 0 & 1 & - 5 & 0 \\ 0 & 0 & 0 & 0 & 4 \end{array}]$
4619	Find the Nullity	[[1,x,3],[-2,10,-9]]	$[\begin{array}{c} 1 & x & 3 \\ - 2 & 10 & - 9 \end{array}]$
4620	Find the Nullity	[[1],[-2]]	$[\begin{array}{c} 1 \\ - 2 \end{array}]$
4621	Find the Nullity	[[-10,4],[5,-2],[20,-8],[-15,6]]	$[\begin{array}{c} - 10 & 4 \\ 5 & - 2 \\ 20 & - 8 \\ - 15 & 6 \end{array}]$
4622	Find the Nullity	[[100],[3]]	$[\begin{array}{c} 100 \\ 3 \end{array}]$
4623	Find the Nullity	[[14,-18,-8,10,6,-6,-14],[-8,12,14,-4,-12,-10,10],[10,-14,-12,10,-12,4,16],[-6,10,16,-2,-14,-8,16],[12,-16,-10,8,8,18,6]]	$[\begin{array}{c} 14 & - 18 & - 8 & 10 & 6 & - 6 & - 14 \\ - 8 & 12 & 14 & - 4 & - 12 & - 10 & 10 \\ 10 & - 14 & - 12 & 10 & - 12 & 4 & 16 \\ - 6 & 10 & 16 & - 2 & - 14 & - 8 & 16 \\ 12 & - 16 & - 10 & 8 & 8 & 18 & 6 \end{array}]$
4624	Find the Nullity	[[17,22,4],[2,9,11],[4,6,13]]	$[\begin{array}{c} 17 & 22 & 4 \\ 2 & 9 & 11 \\ 4 & 6 & 13 \end{array}]$
4625	Find the Nullity	[[2,2,6],[-4,5,-1],[3,7,1]]	$[\begin{array}{c} 2 & 2 & 6 \\ - 4 & 5 & - 1 \\ 3 & 7 & 1 \end{array}]$
4626	Find the Nullity	[[b+c,c+a,a+b],[a,b,c],[1,1,1]]=0	$[\begin{array}{c} b + c & c + a & a + b \\ a & b & c \\ 1 & 1 & 1 \end{array}] = 0$
4627	Determine if Linear	x([[a],[b],[d]])=[[2a+d],[-4b]]	$x ([\begin{array}{c} a \\ b \\ d \end{array}]) = [\begin{array}{c} 2 a + d \\ - 4 b \end{array}]$
4628	Determine if Linear	15[[3,-6,5],[2,-1,0],[-4,7,4]]-5x=30[[-1,-2,1],[5,5,-4],[-3,-2,1]]	$15 [\begin{array}{c} 3 & - 6 & 5 \\ 2 & - 1 & 0 \\ - 4 & 7 & 4 \end{array}] - 5 x = 30 [\begin{array}{c} - 1 & - 2 & 1 \\ 5 & 5 & - 4 \\ - 3 & - 2 & 1 \end{array}]$
4629	Determine if Linear	[[1,0],[0,1]]y[[1,0],[0,0]]=[[3,0],[0,2]]	$[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}] y [\begin{array}{c} 1 & 0 \\ 0 & 0 \end{array}] = [\begin{array}{c} 3 & 0 \\ 0 & 2 \end{array}]$
4630	Evaluate	square root of (1/3)(0.0001)^2+(1/3)(-0.0005)^2+(1/3)(0.0006)^2+(1/3)(-0.0001)^2	$\sqrt{(\frac{1}{3}) {(0.0001)}^{2} + (\frac{1}{3}) {(- 0.0005)}^{2} + (\frac{1}{3}) {(0.0006)}^{2} + (\frac{1}{3}) {(- 0.0001)}^{2}}$
4631	Evaluate	square root of (2-3)^2+(-3-6)^2	$\sqrt{{(2 - 3)}^{2} + {(- 3 - 6)}^{2}}$
4632	Evaluate	square root of (-4-3)^2+(-3-42)	$\sqrt{{(- 4 - 3)}^{2} + (- 3 - 42)}$
4633	Evaluate	square root of 192/121	$\sqrt{\frac{192}{121}}$
4634	Evaluate	square root of 27/64	$\sqrt{\frac{27}{64}}$
4635	Evaluate	square root of 3^2-2^2-6^2	$\sqrt{3^{2} - 2^{2} - 6^{2}}$
4636	Evaluate	square root of 315/7	$\sqrt{\frac{315}{7}}$
4637	Evaluate	square root of 52/100	$\sqrt{\frac{52}{100}}$
4638	Evaluate	(5 square root of 10-2)(4 square root of 6+3)	$(5 \sqrt{10 - 2}) (4 \sqrt{6 + 3})$
4639	Evaluate	(5 square root of 2)(7 square root of 200)	$(5 \sqrt{2}) (7 \sqrt{200})$
4640	Evaluate	(9 square root of 5-5 square root of 6)(3 square root of 5+2 square root of 6)	$(9 \sqrt{5} - 5 \sqrt{6}) (3 \sqrt{5} + 2 \sqrt{6})$
4641	Evaluate	(-(11)-v((-11)^2-4-16123))/(2(-16))	$\frac{- (11) - v ({(- 11)}^{2} - 4 \cdot - 16 \cdot 123)}{2 (- 16)}$
4642	Evaluate	(3 square root of 11)^2	${(3 \sqrt{11})}^{2}$
4643	Evaluate	(-32+ square root of 512)/-32	$\frac{- 32 + \sqrt{512}}{- 32}$
4644	Evaluate	( square root of 0.05(1-0.05))/150	$\frac{\sqrt{0.05 (1 - 0.05)}}{150}$
4645	Evaluate	( square root of 243)/( square root of 3)	$\frac{\sqrt{243}}{\sqrt{3}}$
4646	Evaluate	( square root of 25(100-25))/1250	$\frac{\sqrt{25 (100 - 25)}}{1250}$
4647	Evaluate	( square root of -36 square root of -49)/( square root of -16)	$\frac{\sqrt{- 36} \sqrt{- 49}}{\sqrt{- 16}}$
4648	Evaluate	( square root of 5- square root of 7)/( square root of 35- square root of 34)	$\frac{\sqrt{5} - \sqrt{7}}{\sqrt{35} - \sqrt{34}}$
4649	Evaluate	( fifth root of 9)^11	${(\sqrt[5]{9})}^{11}$
4650	Evaluate	(5750 root of 0.5)^4000	${(\sqrt[5750]{0.5})}^{4000}$
4651	Evaluate	(18+ square root of -324)/(2+ square root of -4)	$\frac{18 + \sqrt{- 324}}{2 + \sqrt{- 4}}$
4652	Evaluate	(2 square root of 351)/351	$\frac{2 \sqrt{351}}{351}$
4653	Evaluate	(-3 square root of 3^2+16)/2	$\frac{- 3 \sqrt{3^{2} + 16}}{2}$
4654	Evaluate	(3+ square root of 5)/(2- square root of 5)	$\frac{3 + \sqrt{5}}{2 - \sqrt{5}}$
4655	Evaluate	(-6- square root of 100)/2	$\frac{- 6 - \sqrt{100}}{2}$
4656	Evaluate	7^3 square root of -64	$7^{3} \sqrt{- 64}$
4657	Evaluate	(9(266178)-3986*403)/( square root of 9(407404)-15888196 square root of 9(22487)-(162409))	$\frac{9 (266178) - 3986 \cdot 403}{\sqrt{9 (407404) - 15888196} \sqrt{9 (22487)} - (162409)}$
4658	Evaluate	v((-6-(-8))^2+(8-6)^2)	$v ({(- 6 - (- 8))}^{2} + {(8 - 6)}^{2})$
4659	Convert to Trigonometric Form	6-(8+3i)	$6 - (8 + 3 i)$
4660	Convert to Trigonometric Form	-6-2i	$- 6 - 2 i$
4661	Convert to Trigonometric Form	-7+7i	$- 7 + 7 i$
4662	Convert to Trigonometric Form	(2+8i)-(6+9i)	$(2 + 8 i) - (6 + 9 i)$
4663	Convert to Trigonometric Form	3-5i	$3 - 5 i$
4664	Convert to Trigonometric Form	-10-2i	$- 10 - 2 i$
4665	Convert to Trigonometric Form	-4 square root of 3+i	$- 4 \sqrt{3} + i$
4666	Convert to Trigonometric Form	-4+0i	$- 4 + 0 i$
4667	Convert to Trigonometric Form	54i	$54 i$
4668	Convert to Trigonometric Form	-5i(4-3i)^2	$- 5 i {(4 - 3 i)}^{2}$
4669	Convert to Trigonometric Form	(4+3i)-(5-7i)	$(4 + 3 i) - (5 - 7 i)$
4670	Convert to Trigonometric Form	(5i)(2+6i)	$(5 i) (2 + 6 i)$
4671	Convert to Trigonometric Form	6-3i+(5+4i)	$6 - 3 i + (5 + 4 i)$
4672	Convert to Trigonometric Form	(-7+4i)-(-9-3i)	$(- 7 + 4 i) - (- 9 - 3 i)$
4673	Convert to Trigonometric Form	(8-7i)(6+7i)	$(8 - 7 i) (6 + 7 i)$
4674	Convert to Trigonometric Form	\|-1-2i\|	$\| - 1 - 2 i \|$
4675	Convert to Trigonometric Form	\|-7-9i\|	$\| - 7 - 9 i \|$
4676	Convert to Trigonometric Form	2/3-i/3	$\frac{2}{3} - \frac{i}{3}$
4677	Convert to Trigonometric Form	i^167	$i^{167}$
4678	Convert to Trigonometric Form	i^22+i^33+i^44+i^55	$i^{22} + i^{33} + i^{44} + i^{55}$
4679	Convert to Trigonometric Form	i^8	$i^{8}$
4680	Convert to Trigonometric Form	square root of 2+ square root of 2i	$\sqrt{2} + \sqrt{2} i$
4681	Convert to Trigonometric Form	square root of 5+i square root of 5	$\sqrt{5} + i \sqrt{5}$
4682	Evaluate	21 root of 12	$\sqrt[21]{12}$
4683	Evaluate	cube root of 17^2	$\sqrt[3]{17^{2}}$
4684	Evaluate	cube root of 10.648	$\sqrt[3]{10.648}$
4685	Evaluate	square root of -81 square root of -144	$\sqrt{- 81} \sqrt{- 144}$
4686	Evaluate	square root of 820	$\sqrt{820}$
4687	Evaluate	square root of 666	$\sqrt{666}$
4688	Evaluate	- square root of 68 square root of 407	$- \sqrt{68} \sqrt{407}$
4689	Evaluate	square root of 4416	$\sqrt{4416}$
4690	Evaluate	- square root of 48.5	$- \sqrt{48.5}$
4691	Evaluate	square root of -49-4	$\sqrt{- 49 - 4}$
4692	Solve Using an Inverse Matrix	10x+5y=4 , -2x=y+4	$10 x + 5 y = 4$ , $- 2 x = y + 4$
4693	Evaluate	square root of -14 square root of -2	$\sqrt{- 14} \sqrt{- 2}$
4694	Evaluate	square root of 16-16	$\sqrt{16 - 16}$
4695	Convert to Trigonometric Form	8i(7-5i)	$8 i (7 - 5 i)$
4696	Write as a Vector Equality	3x-2y=8 , 6y=15x+12	$3 x - 2 y = 8$ , $6 y = 15 x + 12$
4697	Evaluate	square root of 14+6 square root of 5+3+ square root of 5	$\sqrt{14 + 6 \sqrt{5}} + 3 + \sqrt{5}$
4698	Evaluate	square root of 18 square root of 45/10	$\sqrt{18} \sqrt{\frac{45}{10}}$
4699	Evaluate	square root of 1988	$\sqrt{1988}$
4700	Solve Using an Inverse Matrix	e+3f-2g=11 , 2e-f+g=3 , 3e-2f+4g=1	$e + 3 f - 2 g = 11$ , $2 e - f + g = 3$ , $3 e - 2 f + 4 g = 1$