Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
201	Find Reduced Row Echelon Form	[[7,6]]	$[\begin{matrix} 7 & 6 \end{matrix}]$ $[\begin{array}{c} 7 & 6 \end{array}]$
202	Find the Eigenvalues	[[2,1,1],[1,2,1],[1,1,2]]	$⎡ ⎢ ⎣ \begin{matrix} 2 & 1 & 1 1 & 2 & 1 1 & 1 & 2 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{array}]$
203	Find the Characteristic Equation	[[1,3,0,0],[2,2,0,0],[0,0,1,3],[0,0,2,2]]	$⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 1 & 3 & 0 & 0 2 & 2 & 0 & 0 0 & 0 & 1 & 3 0 & 0 & 2 & 2 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦$ $[\begin{array}{c} 1 & 3 & 0 & 0 \\ 2 & 2 & 0 & 0 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 2 & 2 \end{array}]$
204	Find the Characteristic Equation	[[4,1,7,2],[0,3,-1,5],[0,0,8,3],[0,0,0,4]]	$⎡ ⎢ ⎢ ⎢ ⎢ ⎣ \begin{matrix} 4 & 1 & 7 & 2 0 & 3 & - 1 & 5 0 & 0 & 8 & 3 0 & 0 & 0 & 4 \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎥ ⎦$ $[\begin{array}{c} 4 & 1 & 7 & 2 \\ 0 & 3 & - 1 & 5 \\ 0 & 0 & 8 & 3 \\ 0 & 0 & 0 & 4 \end{array}]$
205	Find the Eigenvectors/Eigenspace	A=[[6,-3],[-2,1]]	$A = [\begin{matrix} 6 & - 3 - 2 & 1 \end{matrix}]$ $A = [\begin{array}{c} 6 & - 3 \\ - 2 & 1 \end{array}]$
206	Find the Characteristic Equation	[[2,4,6],[4,5,6],[3,1,-2]]	$⎡ ⎢ ⎣ \begin{matrix} 2 & 4 & 6 4 & 5 & 6 3 & 1 & - 2 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 2 & 4 & 6 \\ 4 & 5 & 6 \\ 3 & 1 & - 2 \end{array}]$
207	Find the Eigenvectors/Eigenspace	A=[[1,0,0],[1,2,0],[-3,5,2]]	$A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 1 & 2 & 0 - 3 & 5 & 2 \end{matrix} ⎤ ⎥ ⎦$ $A = [\begin{array}{c} 1 & 0 & 0 \\ 1 & 2 & 0 \\ - 3 & 5 & 2 \end{array}]$
208	Find the Eigenvectors/Eigenspace	[[1,-1,0],[-1,2,-1],[0,-1,1]]	$⎡ ⎢ ⎣ \begin{matrix} 1 & - 1 & 0 - 1 & 2 & - 1 0 & - 1 & 1 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 1 & - 1 & 0 \\ - 1 & 2 & - 1 \\ 0 & - 1 & 1 \end{array}]$
209	Find the Eigenvalues	[[2,1],[3,4]]	$[\begin{matrix} 2 & 1 3 & 4 \end{matrix}]$ $[\begin{array}{c} 2 & 1 \\ 3 & 4 \end{array}]$
210	Find the Eigenvalues	[[-4,0,1],[3,-6,3],[1,0,-4]]	$⎡ ⎢ ⎣ \begin{matrix} - 4 & 0 & 1 3 & - 6 & 3 1 & 0 & - 4 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} - 4 & 0 & 1 \\ 3 & - 6 & 3 \\ 1 & 0 & - 4 \end{array}]$
211	Find the Eigenvalues	[[6,8,9],[x,8,6],[5,6,5]]	$⎡ ⎢ ⎣ \begin{matrix} 6 & 8 & 9 x & 8 & 6 5 & 6 & 5 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 6 & 8 & 9 \\ x & 8 & 6 \\ 5 & 6 & 5 \end{array}]$
212	Find Reduced Row Echelon Form	[[6,-8,10],[-3/4,1,-5/4]]	$[\begin{matrix} 6 & - 8 & 10 - \frac{3}{4} & 1 & - \frac{5}{4} \end{matrix}]$ $[\begin{array}{c} 6 & - 8 & 10 \\ - \frac{3}{4} & 1 & - \frac{5}{4} \end{array}]$
213	Find the Inverse	[[2,3],[1,1]]	$[\begin{matrix} 2 & 3 1 & 1 \end{matrix}]$ $[\begin{array}{c} 2 & 3 \\ 1 & 1 \end{array}]$
214	Find Reduced Row Echelon Form	[[1,-9,16],[0,0,0]]	$[\begin{matrix} 1 & - 9 & 16 0 & 0 & 0 \end{matrix}]$ $[\begin{array}{c} 1 & - 9 & 16 \\ 0 & 0 & 0 \end{array}]$
215	Find Reduced Row Echelon Form	[[3,-2,7,63],[2,1,-21,28],[1,4,-49,-7]]	$⎡ ⎢ ⎣ \begin{matrix} 3 & - 2 & 7 & 63 2 & 1 & - 21 & 28 1 & 4 & - 49 & - 7 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 3 & - 2 & 7 & 63 \\ 2 & 1 & - 21 & 28 \\ 1 & 4 & - 49 & - 7 \end{array}]$
216	Find Reduced Row Echelon Form	[[7,2,1,0],[3,7,0,1]]	$[\begin{matrix} 7 & 2 & 1 & 0 3 & 7 & 0 & 1 \end{matrix}]$ $[\begin{array}{c} 7 & 2 & 1 & 0 \\ 3 & 7 & 0 & 1 \end{array}]$
217	Find Reduced Row Echelon Form	[[7,2,2],[2,2,7]]	$[\begin{matrix} 7 & 2 & 2 2 & 2 & 7 \end{matrix}]$ $[\begin{array}{c} 7 & 2 & 2 \\ 2 & 2 & 7 \end{array}]$
218	Transpose	[[2,-1,1],[3,1,-2],[-1,2,5]]	$⎡ ⎢ ⎣ \begin{matrix} 2 & - 1 & 1 3 & 1 & - 2 - 1 & 2 & 5 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 2 & - 1 & 1 \\ 3 & 1 & - 2 \\ - 1 & 2 & 5 \end{array}]$
219	Transpose	[[3,1,0],[-1,0,4],[2,2,1]]	$⎡ ⎢ ⎣ \begin{matrix} 3 & 1 & 0 - 1 & 0 & 4 2 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 3 & 1 & 0 \\ - 1 & 0 & 4 \\ 2 & 2 & 1 \end{array}]$
220	Find the Eigenvalues	[[0,1],[-1,0]]	$[\begin{matrix} 0 & 1 - 1 & 0 \end{matrix}]$ $[\begin{array}{c} 0 & 1 \\ - 1 & 0 \end{array}]$
221	Find the Eigenvalues	[[1,1],[-1,1]]	$[\begin{matrix} 1 & 1 - 1 & 1 \end{matrix}]$ $[\begin{array}{c} 1 & 1 \\ - 1 & 1 \end{array}]$
222	Find Reduced Row Echelon Form	[[a,b,1,0],[c,d,0,1]]	$[\begin{matrix} a & b & 1 & 0 c & d & 0 & 1 \end{matrix}]$ $[\begin{array}{c} a & b & 1 & 0 \\ c & d & 0 & 1 \end{array}]$
223	Transpose	[[1,2],[3,4]]	$[\begin{matrix} 1 & 2 3 & 4 \end{matrix}]$ $[\begin{array}{c} 1 & 2 \\ 3 & 4 \end{array}]$
224	Transpose	[[5,2],[3,6]]	$[\begin{matrix} 5 & 2 3 & 6 \end{matrix}]$ $[\begin{array}{c} 5 & 2 \\ 3 & 6 \end{array}]$
225	Find the Eigenvectors/Eigenspace	[[1,2,1],[0,3,1],[0,5,-1]]	$⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 1 0 & 3 & 1 0 & 5 & - 1 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 1 & 2 & 1 \\ 0 & 3 & 1 \\ 0 & 5 & - 1 \end{array}]$
226	Find the Eigenvectors/Eigenspace	[[1,0,1],[0,-1,0],[2,1,-1]]	$⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 1 0 & - 1 & 0 2 & 1 & - 1 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 1 & 0 & 1 \\ 0 & - 1 & 0 \\ 2 & 1 & - 1 \end{array}]$
227	Find the Eigenvectors/Eigenspace	[[1,3],[4,2]]	$[\begin{matrix} 1 & 3 4 & 2 \end{matrix}]$ $[\begin{array}{c} 1 & 3 \\ 4 & 2 \end{array}]$
228	Find the Eigenvectors/Eigenspace	[[1.3,0.4],[-0.2,1.9]]	$[\begin{matrix} 1.3 & 0.4 - 0.2 & 1.9 \end{matrix}]$ $[\begin{array}{c} 1.3 & 0.4 \\ - 0.2 & 1.9 \end{array}]$
229	Find the Eigenvectors/Eigenspace	[[2,1,1],[1,2,1],[1,1,2]]	$⎡ ⎢ ⎣ \begin{matrix} 2 & 1 & 1 1 & 2 & 1 1 & 1 & 2 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 2 \end{array}]$
230	Find the Eigenvectors/Eigenspace	[[-2,-1,-1],[-2,-3,-2],[2,2,1]]	$⎡ ⎢ ⎣ \begin{matrix} - 2 & - 1 & - 1 - 2 & - 3 & - 2 2 & 2 & 1 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} - 2 & - 1 & - 1 \\ - 2 & - 3 & - 2 \\ 2 & 2 & 1 \end{array}]$
231	Find the Eigenvectors/Eigenspace	[[3,0,-1],[2,3,1],[-3,4,5]]	$⎡ ⎢ ⎣ \begin{matrix} 3 & 0 & - 1 2 & 3 & 1 - 3 & 4 & 5 \end{matrix} ⎤ ⎥ ⎦$ $[\begin{array}{c} 3 & 0 & - 1 \\ 2 & 3 & 1 \\ - 3 & 4 & 5 \end{array}]$
232	Find the Characteristic Equation	[[3,2],[4,6]]	$[\begin{matrix} 3 & 2 4 & 6 \end{matrix}]$ $[\begin{array}{c} 3 & 2 \\ 4 & 6 \end{array}]$
233	Find the Eigenvectors/Eigenspace	[[4,-4],[-2,2]]	$[\begin{matrix} 4 & - 4 - 2 & 2 \end{matrix}]$ $[\begin{array}{c} 4 & - 4 \\ - 2 & 2 \end{array}]$
234	Find the Eigenvectors/Eigenspace	[[5,0],[2,3]]	$[\begin{matrix} 5 & 0 2 & 3 \end{matrix}]$ $[\begin{array}{c} 5 & 0 \\ 2 & 3 \end{array}]$
235	Find the Eigenvectors/Eigenspace	[[5,3],[3,5]]	$[\begin{matrix} 5 & 3 3 & 5 \end{matrix}]$ $[\begin{array}{c} 5 & 3 \\ 3 & 5 \end{array}]$
236	Find the Null Space	[[0,4,-3,-1],[4,4,-2,-2],[-1,-1,1,-1],[0,2,1,3]]	$[\begin{array}{c} 0 & 4 & - 3 & - 1 \\ 4 & 4 & - 2 & - 2 \\ - 1 & - 1 & 1 & - 1 \\ 0 & 2 & 1 & 3 \end{array}]$
237	Find the Eigenvectors/Eigenspace	[[8,6],[-3,2]]	$[\begin{array}{c} 8 & 6 \\ - 3 & 2 \end{array}]$
238	Find the Null Space	[[2,1],[1,3]]	$[\begin{array}{c} 2 & 1 \\ 1 & 3 \end{array}]$
239	Find the Null Space	[[1,4,0,3,0],[0,0,1,-3,0],[0,0,0,0,-1]]	$[\begin{array}{c} 1 & 4 & 0 & 3 & 0 \\ 0 & 0 & 1 & - 3 & 0 \\ 0 & 0 & 0 & 0 & - 1 \end{array}]$
240	Find the Null Space	s=[[2,4,6,4],[2,5,7,6],[2,3,5,2]]	$s = [\begin{array}{c} 2 & 4 & 6 & 4 \\ 2 & 5 & 7 & 6 \\ 2 & 3 & 5 & 2 \end{array}]$
241	Find the Null Space	[[7,6,2],[6,3,1],[5,5,6]]	$[\begin{array}{c} 7 & 6 & 2 \\ 6 & 3 & 1 \\ 5 & 5 & 6 \end{array}]$
242	Find the Norm	[[-3,0,-6],[-2,3,4]]	$[\begin{array}{c} - 3 & 0 & - 6 \\ - 2 & 3 & 4 \end{array}]$
243	Find the Rank	[[1,0,-4,0,-2,3],[0,1,7,-1,0,5],[0,0,0,0,1,0],[0,0,0,0,0,0]]	$[\begin{array}{c} 1 & 0 & - 4 & 0 & - 2 & 3 \\ 0 & 1 & 7 & - 1 & 0 & 5 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{array}]$
244	Find the Eigenvectors/Eigenspace	[[1,0],[6,-1]]	$[\begin{array}{c} 1 & 0 \\ 6 & - 1 \end{array}]$
245	Solve Using an Inverse Matrix	2x+2y=-16 , y=-x-8	$2 x + 2 y = - 16$ , $y = - x - 8$
246	Evaluate	square root of 4+76-4	$\sqrt{4 + 76 - 4}$
247	Convert to Trigonometric Form	(-3-5i)-(4+2i)	$(- 3 - 5 i) - (4 + 2 i)$
248	Convert to Trigonometric Form	2+7i+(-6+i)	$2 + 7 i + (- 6 + i)$
249	Evaluate	(11+ square root of 15)(11- square root of 15)	$(11 + \sqrt{15}) (11 - \sqrt{15})$
250	Evaluate	square root of (-7)^2+(5)^2	$\sqrt{{(- 7)}^{2} + {(5)}^{2}}$
251	Find the Nullity	[[1,2,2,3],[-1,-3,3,2],[2,-3,4,6]]	$[\begin{array}{c} 1 & 2 & 2 & 3 \\ - 1 & - 3 & 3 & 2 \\ 2 & - 3 & 4 & 6 \end{array}]$
252	Find the Nullity	[[1,0,1,0,6],[1,1,2,2,0],[0,0,1,0,0],[0,0,0,0,0]]	$[\begin{array}{c} 1 & 0 & 1 & 0 & 6 \\ 1 & 1 & 2 & 2 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{array}]$
253	Find the Null Space	[[2],[1],[4]]	$[\begin{array}{c} 2 \\ 1 \\ 4 \end{array}]$
254	Find the Nullity	[[1,-1,3],[6,7,-3],[9,4,6]]	$[\begin{array}{c} 1 & - 1 & 3 \\ 6 & 7 & - 3 \\ 9 & 4 & 6 \end{array}]$
255	Determine if Linear	[[1,5],[4,8]]*[[x],[y]]=[[-20],[-44]]	$[\begin{array}{c} 1 & 5 \\ 4 & 8 \end{array}] \cdot [\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} - 20 \\ - 44 \end{array}]$
256	Determine if Linear	x-[[0,1,5,-6],[5,8,7,-1]]=[[1,2,3,6],[-8,-4,-2,-3]]	$x - [\begin{array}{c} 0 & 1 & 5 & - 6 \\ 5 & 8 & 7 & - 1 \end{array}] = [\begin{array}{c} 1 & 2 & 3 & 6 \\ - 8 & - 4 & - 2 & - 3 \end{array}]$
257	Project Using the Transformation	A=[[1],[5],[6]] , x=[[1,-2,8]]	$A = [\begin{array}{c} 1 \\ 5 \\ 6 \end{array}]$ , $x = [\begin{array}{c} 1 & - 2 & 8 \end{array}]$
258	Simplify the Matrix	[[1,0,1],[-1,21,0]] , [[2,2,-2],[-3,4,3]]	$[\begin{array}{c} 1 & 0 & 1 \\ - 1 & 21 & 0 \end{array}]$ , $[\begin{array}{c} 2 & 2 & - 2 \\ - 3 & 4 & 3 \end{array}]$
259	Find the Kernel	S([[a],[b],[c]])=[[a-b-c],[a-b-c],[a-b+c]]	$S ([\begin{array}{c} a \\ b \\ c \end{array}]) = [\begin{array}{c} a - b - c \\ a - b - c \\ a - b + c \end{array}]$
260	Determine if Linear	[[x],[y]]=[[y],[x]]	$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} y \\ x \end{array}]$
261	Evaluate	4 cube root of 24	$4 \sqrt[3]{24}$
262	Find the Intersection of the Sets	A=(3,4,6,1) , B=(0,9,8,7,1)	$A = (3, 4, 6, 1)$ , $B = (0, 9, 8, 7, 1)$
263	Find the Determinant of the Resulting Matrix	[[0.30,0.20,0.30],[0.40,0.30,0.30],[0.30,0.30,0.20]]-[[1,0,0],[0,1,0],[0,0,1]]	$[\begin{array}{c} 0.3 & 0.2 & 0.3 \\ 0.4 & 0.3 & 0.3 \\ 0.3 & 0.3 & 0.2 \end{array}] - [\begin{array}{c} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}]$
264	Evaluate	-12 square root of 1+5	$- 12 \sqrt{1 + 5}$
265	Find the Power Set	(0,2)	$(0, 2)$
266	Find the Power Set	(0,5)	$(0, 5)$
267	Find the Power Set	(1,4)	$(1, 4)$
268	Find the Inverse of the Resulting Matrix	[[8,93,0.01],[44,575,5],[1,0.1,0.1]][[8,24,5],[8,9,6],[0.1,1,2]]	$[\begin{array}{c} 8 & 93 & 0.01 \\ 44 & 575 & 5 \\ 1 & 0.1 & 0.1 \end{array}] [\begin{array}{c} 8 & 24 & 5 \\ 8 & 9 & 6 \\ 0.1 & 1 & 2 \end{array}]$
269	Find the Power Set	(-1,3)	$(- 1, 3)$
270	Find the Power Set	(-2,3)	$(- 2, 3)$
271	Find the Power Set	(0,9)	$(0, 9)$
272	Find the Power Set	(3,-4)	$(3, - 4)$
273	Find the Power Set	(2,-3)	$(2, - 3)$
274	Find the Power Set	(4,2)	$(4, 2)$
275	Find the Power Set	(3,2)	$(3, 2)$
276	Find the Dimensions	[[4,5,9,-2],[6,5,1,12],[3,4,8,-3]]	$[\begin{array}{c} 4 & 5 & 9 & - 2 \\ 6 & 5 & 1 & 12 \\ 3 & 4 & 8 & - 3 \end{array}]$
277	Find the Dimensions	[[1,2],[5,5],[10,3],[4,6],[7,0]]	$[\begin{array}{c} 1 & 2 \\ 5 & 5 \\ 10 & 3 \\ 4 & 6 \\ 7 & 0 \end{array}]$
278	Find the Dimensions	[[-2,3,1,4]]	$[\begin{array}{c} - 2 & 3 & 1 & 4 \end{array}]$
279	Find the Dimensions	[[1,2,3,4],[40,-11,-55.7,-95.99]]	$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 40 & - 11 & - 55.7 & - 95.99 \end{array}]$
280	Find the Dimensions	[[1,2]]	$[\begin{array}{c} 1 & 2 \end{array}]$
281	Find the Dimensions	[[4,2],[6,7]]	$[\begin{array}{c} 4 & 2 \\ 6 & 7 \end{array}]$
282	Find the Domain	f(x)=-x^4+4x^2-x-5	$f (x) = - x^{4} + 4 x^{2} - x - 5$
283	Find the Domain	f(x)=1.5x-3	$f (x) = 1.5 x - 3$
284	Find the Domain	f(x)=2x-3	$f (x) = 2 x - 3$
285	Find the Domain	f(x)=4x^2+1/x	$f (x) = 4 x^{2} + \frac{1}{x}$
286	Find the Domain	(f(x)(x^2-7x+10))/(x^2-25)	$\frac{f (x) (x^{2} - 7 x + 10)}{x^{2} - 25}$
287	Find the Domain	f(x)=(x-1)(x+4)(x-5)	$f (x) = (x - 1) (x + 4) (x - 5)$
288	Find the Domain	f(x)=(x^3-x^2+1)/(\|x\|)	$f (x) = \frac{x^{3} - x^{2} + 1}{\| x \|}$
289	Find the Domain	f(x)=1/3(x)+4	$f (x) = \frac{1}{3} (x) + 4$
290	Find the Domain	f(x)=5/3*(4/5)^x	$f (x) = \frac{5}{3} \cdot {(\frac{4}{5})}^{x}$
291	Find the Domain	d=v(x^2-x+(y^2-y))*22	$d = v (x^{2} - x + (y^{2} - y)) \cdot 22$
292	Find the Domain	f(x)=-x^2	$f (x) = - x^{2}$
293	Find the Domain	9x+8y=29	$9 x + 8 y = 29$
294	Find the Domain	6x-3y=12	$6 x - 3 y = 12$
295	Find the Domain	c(A)^t=(1/C)a^t	$c {(A)}^{t} = (\frac{1}{C}) a^{t}$
296	Find the Domain	8x-3y+12=0	$8 x - 3 y + 12 = 0$
297	Find the Domain	9x^3+2x-8x^3-3x	$9 x^{3} + 2 x - 8 x^{3} - 3 x$
298	Find the Domain	9x-5-2x=16	$9 x - 5 - 2 x = 16$
299	Find the Domain	7x+8y=51.30	$7 x + 8 y = 51.3$
300	Find the Domain	7x-4y=-3	$7 x - 4 y = - 3$