document.write( "Question 64626This question is from textbook Holt Algebra 2 w/Trig
\n" ); document.write( ": I have tried for 2 days to solve this one! I have the answers, and they do solve the equations, so they are correct. However, I am unable to produce the answers using matrix transformations. Any step-by-step help would be appreciated.\r
\n" ); document.write( "\n" ); document.write( "-2r + 6s -3t + 3v = -5
\n" ); document.write( "4r - 3s + 2t -v = -3
\n" ); document.write( "-3r - 4s - 3t + 4v = -15
\n" ); document.write( "5r + 2s - 2t + 3v = -20\r
\n" ); document.write( "\n" ); document.write( "The solution is r,s,t,v = -2,1,3,-2 respectively. \n" ); document.write( "
Algebra.Com's Answer #45211 by Fermat(136)\"\" \"About 
You can put this solution on YOUR website!
I'm using Gauss-Jordan elimination method. You could follow these steps to produce your inverse matrix.\r
\n" ); document.write( "\n" ); document.write( "The augmented matrix is shown below, in sets of 4 equations, or rows.
\n" ); document.write( "The row operations, following a set of 4 eqns, apply to that set of eqns, with the result being in the following set of 4 eqns.\r
\n" ); document.write( "\n" ); document.write( "-2 6 -3 3 | -5 ---(1)
\n" ); document.write( " 4 -3 2 -1 | -3 ---(2)
\n" ); document.write( "-3 -4 -3 4 |-15 ---(3)
\n" ); document.write( " 5 2 -2 3 |-20 ---(4)\r
\n" ); document.write( "\n" ); document.write( "(3)x2, (4)x2\r
\n" ); document.write( "\n" ); document.write( "-2 6 -3 3 | -5 ---(5)
\n" ); document.write( " 4 -3 2 -1 | -3 ---(6)
\n" ); document.write( "-6 -8 -6 8 |-30 ---(7)
\n" ); document.write( "10 4 -4 6 |-40 ---(8)\r
\n" ); document.write( "\n" ); document.write( "(6) + 2x(5), (7) - 3x(5), (8) + 5x(5)\r
\n" ); document.write( "\n" ); document.write( "-2 6 -3 3 | -5 ---(9)
\n" ); document.write( " 0 9 -4 5 |-13 ---(10)
\n" ); document.write( " 0-26 3 -1 |-15 ---(11)
\n" ); document.write( " 0 34-19 21|-65 ---(12)\r
\n" ); document.write( "\n" ); document.write( "(12) + (11), (11) + 3x(10)\r
\n" ); document.write( "\n" ); document.write( "-2 6 -3 3 | -5 ---(13)
\n" ); document.write( " 0 9 -4 5 |-13 ---(14)
\n" ); document.write( " 0 1 -9 14 |-54 ---(15)
\n" ); document.write( " 0 8-16 20 |-80 ---(16)\r
\n" ); document.write( "\n" ); document.write( "(14) - 9x(15), (16) - 8x(15)\r
\n" ); document.write( "\n" ); document.write( "-2 6 -3 3 | -5 ---(17)
\n" ); document.write( " 0 9 77-121|473 ---(18)
\n" ); document.write( " 0 1 -9 14 |-54 ---(19)
\n" ); document.write( " 0 0 56-92 |352 ---(20)\r
\n" ); document.write( "\n" ); document.write( "(18) - (20), (20)÷4\r
\n" ); document.write( "\n" ); document.write( "-2 6 -3 3 | -5 ---(21)
\n" ); document.write( " 0 0 21-29 |473 ---(22)
\n" ); document.write( " 0 1 -9 14 |-54 ---(23)
\n" ); document.write( " 0 0 14-23 | 88 ---(24)\r
\n" ); document.write( "\n" ); document.write( "(22) - (24)\r
\n" ); document.write( "\n" ); document.write( "-2 6 -3 3 | -5 ---(25)
\n" ); document.write( " 0 0 7 -6 | 33 ---(26)
\n" ); document.write( " 0 1 -9 14 |-54 ---(27)
\n" ); document.write( " 0 0 14-23 | 88 ---(28)\r
\n" ); document.write( "\n" ); document.write( "(28) - 2x(26)\r
\n" ); document.write( "\n" ); document.write( "-2 6 -3 3 | -5 ---(29)
\n" ); document.write( " 0 0 7 -6 | 33 ---(30)
\n" ); document.write( " 0 1 -9 14 |-54 ---(31)
\n" ); document.write( " 0 0 0-11 | 22 ---(32)\r
\n" ); document.write( "\n" ); document.write( "(32)÷ -11,\r
\n" ); document.write( "\n" ); document.write( "-2 6 -3 3 | -5 ---(33)
\n" ); document.write( " 0 0 7 -6 | 33 ---(34)
\n" ); document.write( " 0 1 -9 14 |-54 ---(35)
\n" ); document.write( " 0 0 0 1 | 2 ---(36)\r
\n" ); document.write( "\n" ); document.write( "(33) - 3x(36), (34) + 6x(36), (35) - 14x(36)\r
\n" ); document.write( "\n" ); document.write( "-2 6 -3 0 | 1 ---(37)
\n" ); document.write( " 0 0 7 0 | 21 ---(38)
\n" ); document.write( " 0 1 -9 0 |-26 ---(39)
\n" ); document.write( " 0 0 0 1 | 2 ---(40)\r
\n" ); document.write( "\n" ); document.write( "(38)÷7,\r
\n" ); document.write( "\n" ); document.write( "-2 6 -3 0 | 1 ---(41)
\n" ); document.write( " 0 0 1 0 | 3 ---(42)
\n" ); document.write( " 0 1 -9 0 |-26 ---(43)
\n" ); document.write( " 0 0 0 1 | 2 ---(44)\r
\n" ); document.write( "\n" ); document.write( "(41) + 3x(42), (43) + 9x(42)\r
\n" ); document.write( "\n" ); document.write( "-2 6 0 0 | 10 ---(45)
\n" ); document.write( " 0 0 1 0 | 3 ---(46)
\n" ); document.write( " 0 1 0 0 | 1 ---(47)
\n" ); document.write( " 0 0 0 1 | 2 ---(48)\r
\n" ); document.write( "\n" ); document.write( "(45) - 6x(47)\r
\n" ); document.write( "\n" ); document.write( "-2 0 0 0 | 4 ---(49)
\n" ); document.write( " 0 0 1 0 | 3 ---(50)
\n" ); document.write( " 0 1 0 0 | 1 ---(51)
\n" ); document.write( " 0 0 0 1 | 2 ---(52)\r
\n" ); document.write( "\n" ); document.write( "(49)÷ -2\r
\n" ); document.write( "\n" ); document.write( " 1 0 0 0 | -2 ---(53)
\n" ); document.write( " 0 0 1 0 | 3 ---(54)
\n" ); document.write( " 0 1 0 0 | 1 ---(55)
\n" ); document.write( " 0 0 0 1 | 2 ---(56)\r
\n" ); document.write( "\n" ); document.write( "Rearrange,\r
\n" ); document.write( "\n" ); document.write( " 1 0 0 0 | -2 ---(57)
\n" ); document.write( " 0 1 0 0 | 1 ---(58)
\n" ); document.write( " 0 0 1 0 | 3 ---(59)
\n" ); document.write( " 0 0 0 1 | 2 ---(60)\r
\n" ); document.write( "\n" ); document.write( "The solution can now be read off as (-2, 1, 3, -2)
\n" ); document.write( "==================================================
\n" ); document.write( "The inverse matrix is,
\n" ); document.write( "|-29 -12 -9 3|
\n" ); document.write( "|33 22 -11 -11|
\n" ); document.write( "|181 256 19 -121|
\n" ); document.write( "|147 196 35 -77|
\n" ); document.write( "with a coefficient of (1/154). \n" ); document.write( "
\n" );