Math at eNotes
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The latest questions and answers, from members following Math at eNotes.Sat, 13 Feb 2016 17:22:30 PSTen-usLets take an example for better understanding matrix `A`...
http://www.enotes.com/homework-help/how-find-inverse-matrix-by-using-elementary-row-258286
Lets take an example for better understanding matrix `A` =`[[1,2],[2,-1]]` We can write `A` as `IA` , `I` is an identity matrix. `A = AI` Now, we use elementary operations to find `A^-1` . Here we need to change `AI` as `IA^-1` We should use row operations for both matrices `[[1,2],[2,-1]] [[1,0],[0,1]]` Multiply the first row by 2 and subtract it from second row `[[1,2],[0,-5]] [[1,0],[-2,1]] ` Divide second row by (-5) `[[1,2],[0,1]]...http://www.enotes.com/homework-help/how-find-inverse-matrix-by-using-elementary-row-258286Sat, 13 Feb 2016 17:22:30 PST`3x+2y-z+w=0` `x-y+4z+2w=25` `-2x+y+2z-w=2` `x+y+z+w=6` The above system...
http://www.enotes.com/homework-help/3x-2y-z-w-0-x-y-4z-2w-25-2x-y-2z-w-2-x-y-z-w-6-622674
`3x+2y-z+w=0` `x-y+4z+2w=25` `-2x+y+2z-w=2` `x+y+z+w=6` The above system of equations can be represented by the coefficient matrix A and right hand side vector b as follows: `A=[[3,2,-1,1],[1,-1,4,2],[-2,1,2,-1],[1,1,1,1]]` `b=[[0],[25],[2],[6]]` The augmented matrix can be written as: `[A b]=[[3,2,-1,1,0],[1,-1,4,2,25],[-2,1,2,-1,2],[1,1,1,1,6]]` Now let's bring the above matrix in row-echelon form by performing various row operations,...http://www.enotes.com/homework-help/3x-2y-z-w-0-x-y-4z-2w-25-2x-y-2z-w-2-x-y-z-w-6-622674Sat, 13 Feb 2016 10:43:06 PST`x-4y+3z-2w=9` `3x-2y+z-4w=-13` `-4x+3y-2z+w=-4` `-2x+y-4z+3w=-10` The...
http://www.enotes.com/homework-help/x-4y-3z-2w-9-3x-2y-z-4w-13-4x-3y-2z-w-4-2x-y-4z-622675
`x-4y+3z-2w=9` `3x-2y+z-4w=-13` `-4x+3y-2z+w=-4` `-2x+y-4z+3w=-10` The above system of equations can be represented by the coefficient matrix A and right hand side matrix b as follows: A=`[[1,-4,3,-2],[3,-2,1,-4],[-4,3,-2,1],[-2,1,-4,3]]` b=`[[9],[-13],[-4],[-10]]` The augmented matrix can be written as, `[[A,b]]=[[1,-4,3,-2,9],[3,-2,1,-4,-13],[-4,3,-2,1,-4],[-2,1,-4,3,-10]]` Now lets, perform the various row operations to bring the above...http://www.enotes.com/homework-help/x-4y-3z-2w-9-3x-2y-z-4w-13-4x-3y-2z-w-4-2x-y-4z-622675Sat, 13 Feb 2016 08:13:46 PSTWrite the numbers in a column as mentioned below...
http://www.enotes.com/homework-help/you-multiply-2973-2095-how-would-you-set-out-621613
Write the numbers in a column as mentioned below 2 9 7 3 X 2 0 9 5 Lets now find out the numbers which we need to add in column by multiplication. 1. Multiply 2973 by the unit's digit of second number i.e. 5, we get 14865. This is the first number of our column. 2. Multiply 2973 by 90,9 is in tens place. we get 267570. This is the second number of the column 3. Next digit is 0. So the...http://www.enotes.com/homework-help/you-multiply-2973-2095-how-would-you-set-out-621613Sat, 13 Feb 2016 03:26:33 PSTWe want to find the equation of the line passing through the origin that...
http://www.enotes.com/homework-help/find-equation-line-passing-through-0-0-making-an-622413
We want to find the equation of the line passing through the origin that makes an angle of arctan=1/2 with the line 3y=2x: The slope of the given line is 2/3, and the given line also passes through the origin. The angle between the lines is related by the following: `tan theta = (m_1-m_2)/(1+m_1m_2) ` Since the angle is arctan (1/2), we know that `tan theta = 1/2 ` Then ` 1/2=(m-2/3)/(1+m*2/3) ` where m is the slope of the required line. So...http://www.enotes.com/homework-help/find-equation-line-passing-through-0-0-making-an-622413Sat, 13 Feb 2016 03:15:54 PSTWe are given the graph of the function `f(x)=-x^2-3x+10 ` and we are...
http://www.enotes.com/homework-help/curve-included-f-x-10-3x-x2-x-squared-how-find-621740
We are given the graph of the function `f(x)=-x^2-3x+10 ` and we are asked to find the points a,b, and c as indicated on the graph. Note that a and b are the x-intercepts, while c is the y-intercept. (1) c is the easiest to find: the y-intercept occurs when x=0. Then f(0)=10, so the point c is at (0,10). (2) The x-intercepts can be found in a few different ways. Since the quadratic function has x-intercepts, then the roots or zeroes of the...http://www.enotes.com/homework-help/curve-included-f-x-10-3x-x2-x-squared-how-find-621740Sat, 13 Feb 2016 02:42:00 PSTWe are given a rectangular canvas with area 180 square inches with a...
http://www.enotes.com/homework-help/marisol-painting-piece-canvas-that-has-an-area-180-621548
We are given a rectangular canvas with area 180 square inches with a length 5/4 as long as the width and we are asked to find the dimensions: Area = length times width, so we let w=width in inches and l=5/4w=length in inches. Then `w(5/4 w)=180 ` `5/4 w^2=180 ` `w^2=180 * 4/5 ` `w^2=144 ` Since the width must be positive, w=12. Then `l=5/4 w=5/4 * 12=15 ` The dimensions are 12" by 15" Check: 12x15=180 as required.http://www.enotes.com/homework-help/marisol-painting-piece-canvas-that-has-an-area-180-621548Sat, 13 Feb 2016 02:32:45 PSTWe are asked to find the equation of the line through the point (1,-4)...
http://www.enotes.com/homework-help/find-equation-line-that-passes-through-point-1-4-622502
We are asked to find the equation of the line through the point (1,-4) and perpendicular to the line x=4: To write an equation of a line we need either a point and the slope, or two points. Here we are given a point so it suffices to find the slope. Since the line x=4 has no slope (the slope is undefined for a vertical line), the line perpendicular will have slope m=0 (a horizontal line.) Thus we have a line with slope 0 going through the...http://www.enotes.com/homework-help/find-equation-line-that-passes-through-point-1-4-622502Sat, 13 Feb 2016 02:26:04 PSTHere are some ways to describe slope: (1) Verbally slope indicates the...
http://www.enotes.com/homework-help/what-three-ways-describe-slope-622614
Here are some ways to describe slope: (1) Verbally slope indicates the steepness of a line (the sign indicates direction and the absolute value describes the steepness -- the larger the absolute value the steeper the graph.) This is related to the grade of a hill or the pitch of a roof. (2) Algebraically slope is typically represented by m: for instance the equation of a line can be written as y=mx+b where m represents the slope. Also the...http://www.enotes.com/homework-help/what-three-ways-describe-slope-622614Sat, 13 Feb 2016 02:21:14 PSTThe augmented matrix is `[[1,1,4,5],[2,1,-1,9]]` On applying `R_1 -gt...
http://www.enotes.com/homework-help/x-y-4z-5-2x-y-z-9-use-matricies-solve-system-622681
The augmented matrix is `[[1,1,4,5],[2,1,-1,9]]` On applying `R_1 -gt 2R_1 - R_2` we get `[[1,1,4,5],[0,1,9,1]] ` On applying `R_1 -gt R_1 - R_2` we get `[[1,0,-5,4],[0,1,9,1]]` The corresponding system is `x - 5z = 4` `y + 9z = 1` Let `k` be any real number and `z = k` . Now substitute `z` value in above equations and find the values of `x` and `y` in terms of `k` . `x - 5z = 4 ` `x = 4 + 5z = 4 + 5k` `y+ 9z = 1` `y = 1 -9 z = 1 - 9k`...http://www.enotes.com/homework-help/x-y-4z-5-2x-y-z-9-use-matricies-solve-system-622681Fri, 12 Feb 2016 10:25:18 PSTThe augmented matrix is `[[1,2,1,8],[3,7,6,26]]` On applying `R_2 -gt...
http://www.enotes.com/homework-help/x-2y-z-8-3x-7y-6z-26-use-matricies-solve-system-622680
The augmented matrix is `[[1,2,1,8],[3,7,6,26]]` On applying `R_2 -gt R_2 - 3R_1` we get `[[1,2,1,8],[0,1,3,2]]` On applying `R_1 -gt R_1 - 2R_2 ` we get `[[1,0,-5,4],[0,1,3,2]]` The corresponding system is `x -5z = 4` `y +3z = 2` Let `k ` is any real number and` z = k` , now substitute `z ` value in the above equations to find `x` and `y` values. `x - 5z = 4` `x = 4 + 5z = 4 + 5k` `y +3z = 2` `y = 2- 3z = 2 - 3k` `therefore` the solution set...http://www.enotes.com/homework-help/x-2y-z-8-3x-7y-6z-26-use-matricies-solve-system-622680Fri, 12 Feb 2016 05:52:00 PST`2x-y+3z=24` `2y-z=14` `7x-5y=6` Write the equations as,...
http://www.enotes.com/homework-help/2x-y-3z-24-2y-z-14-7x-5y-6-use-matricies-solve-622683
`2x-y+3z=24` `2y-z=14` `7x-5y=6` Write the equations as, `[[2,-1,3,|24],[0,2,-1,|14],[7,-5,0,|6]]` Make the pivot in the first column by dividing the First row by 2, `[[1,-1/2,3/2,|12],[0,2,-1,|14],[7,-5,0,|6]]` Multiply the first row by 7, `[[7,-7/2,21/2,|84],[0,2,-1,|14],[7,-5,0,|6]]` Subtract the 1st row from the 3rd row and restore it, `[[1,-1/2,3/2,|12],[0,2,-1,|14],[0,-3/2,-21/2,|-78]]` Make the pivot in the second column by dividing the...http://www.enotes.com/homework-help/2x-y-3z-24-2y-z-14-7x-5y-6-use-matricies-solve-622683Fri, 12 Feb 2016 05:38:24 PSTThe augmented matrix `[[1,2,0],[1,1,6],[3,-2,8]]` On applying `R_2 -gt...
http://www.enotes.com/homework-help/x-2y-0-x-y-6-3x-2y-8-use-matricies-solve-system-622673
The augmented matrix `[[1,2,0],[1,1,6],[3,-2,8]]` On applying `R_2 -gt R_1 - R_2 ` we get `[[1,2,0],[0,1,-6],[3,-2,8]]` On applying `R_3 -gt 3R_1 - R_3 ` we get `[[1,2,0],[0,1,-6],[0,8,-8]]` On applying `R_3 -gt (R_3)/8` we get `[[1,2,0],[0,1,-6],[0,1,-1]]` On applying `R_3 -gt R_3 - R_2` we get `[[1,2,0],[0,1,-6],[0,0,5]]` The corresponding system is `x + 2y = 0` `y = -6` `0(x) + 0(y) = 5` No `x ` and `y ` value satisfy the last equation....http://www.enotes.com/homework-help/x-2y-0-x-y-6-3x-2y-8-use-matricies-solve-system-622673Fri, 12 Feb 2016 05:20:16 PSTThe augmented matrix is `[[-1,1,-22],[3,4,4],[4,-8,32]]` On applying...
http://www.enotes.com/homework-help/x-y-22-3x-4y-4-4x-8y-32-use-matricies-solve-622672
The augmented matrix is `[[-1,1,-22],[3,4,4],[4,-8,32]]` On applying `R_1 -gt -R_1 ` and `R_3 -gt (R_3)/4` we get (means inverse the sign of first row and divide the third row by 4) `[[1,-1,22],[3,4,4],[1,-2,8]]` On applying `R_2 -gt 3R_1 - R_2` and `R_3 -gt R_3 - R_1` we get `[[1,-1,22],[0,-7,62],[0,-1,-14]]` On applying `R_3 -gt 7R_3 - R_2` we get `[[1,-1,22],[0,-7,62],[0,0,-160]]` On applying `R_2 -gt (R_2)/(-7) ` we get...http://www.enotes.com/homework-help/x-y-22-3x-4y-4-4x-8y-32-use-matricies-solve-622672Fri, 12 Feb 2016 04:59:32 PSTThe augmented matrix is `[[-1,1,-1,-14],...
http://www.enotes.com/homework-help/x-y-z-14-2x-y-z-21-3x-2y-z-19-use-matricies-solve-622684
The augmented matrix is `[[-1,1,-1,-14], [2,-1,1,21],[3,2,1,19]] ` On applying `R_1 -gt R_1 +R_2` we get (means changing 1st row as the sum of of first and second row) `[[1,0,0,7],[2,-1,1,21],[3,2,1,19]] ` On applying `R_2 -gt R_2 - 2R_1` we get `[[1,0,0,7], [0,-1,1,7], [3,2,1,19]] ` On applying `R_2 -gt -R_2` and `R_3 -gt R_3 - 3R_1` we get `[[1,0,0,7],[0,1,-1,-7],[0,2,1,-2]] ` On applying `R_3 -gt R_3 - 2R_2` we get...http://www.enotes.com/homework-help/x-y-z-14-2x-y-z-21-3x-2y-z-19-use-matricies-solve-622684Fri, 12 Feb 2016 04:15:26 PST