math_matrix_doubt_questionsFrequently asked Questions: Matrix and Determinants
Matrix and Determinants
Question: Show that|a+babaa+ccbcb+c|=4abc AnswerLHS=|a+babaa+ccbcb+c|R1R1-R2-R3=|0-2c-2caa+ccbcb+c|C2C2-C3=|00-2caacb-bb+c|=(-2c)(-ab-ab)=4abc=RHS
Question: Show that|1logxylogxzlogyx1logyzlogzxlogyy1|=0 AnswerLHS=|1logxylogxzlogyx1logyzlogzxlogyy1|=|logxxlogxylogxzlogyxlogyylogyzlogzxlogzylogzz|=|logxlogxlogylogxlogzlogxlogxlogylogylogylogzlogylogxlogzlogylogzlogzlogx|=1logxlogylogz|logxlogylogzlogxlogylogzlogxlogylogz|=1logxlogylogz×0=0=RHS
Question: If|4+x4-x4-x4-x4+x4-x4-x4-x4+x|=0 Find x Answer|4+x4-x4-x4-x4+x4-x4-x4-x4+x|=0C2C2-C3|4+x04-x4-x2x4-x4-x-2x4+x|=0C1C1+C2|4+x04-x4+x2x4-x4-3x-2x4+x|=0R1R1-R2|0-2x04+x2x4-x4-3x-2x4+x|=02x[(4+x)(4+x)-(4-x)(4-3x)]=0x=0Answeror16+8x+x2-16-3x2+16x=02x2-24x=02x(x-12)=0x=12Answer
Questionwithout expanding show that|b+cbcb2c2c+acac2a2a+baba2b2|=0 AnswerLHS=|b+cbcb2c2c+acac2a2a+baba2b2|aR1,bR2,cR3=1abc|a(b+c)abcab2c2b(c+a)bcabc2a2c(a+b)cabca2b2|takeabccommonfromC3=abcabc|ab+caabcbcbc+abbcacaca+bccabab|C1C1+C3=|ab+bc+caabcbcab+bc+caabccaab+bc+caabcab|as all the values in C1 is same and all the values in C2is same so |ab+bc+caabcbcab+bc+caabccaab+bc+caabcab|=0So|b+cbcb2c2c+acac2a2a+baba2b2|=0
Questionwithout expanding show that|0ab-a0c-b-c0|=0 AnswerLHS=|0ab-a0c-b-c0|cR1,-bR2,aR3=-1abc|0cabcba0-bc-ab-ca0|R1R1+R2+R3=-1abc|000ba0-bc-ab-ca0|As all the values of R1 is 0 (zero), so -1abc|000ba0-bc-ab-ca0|=0 So |0ab-a0c-b-c0|=0