Advertisements
Advertisements
Question
Solve the following equation:
`|(x + 2, x + 6, x - 1),(x + 6, x - 1, x + 2),(x - 1, x + 2, x + 6)|` = 0
Advertisements
Solution
`|(x + 2, x + 6, x - 1),(x + 6, x - 1, x + 2),(x - 1, x + 2, x + 6)|` = 0
By R2 – R1 and R3 – R1, we get,
`|(x + 2, x + 6, x - 1),(4, -7, 3),(-3, -4, 7)|` = 0
By C2 – C1 and C3 – C1, we get,
`|(x + 2, 4, -3),(4, -11, -1),(-3, -1, 10)|` = 0
∴ (x + 2)( –110 – 1) – 4 (40 – 3) – 3 ( –4 – 33) = 0
∴ (x + 2)( – 111) – 4 (37) – 3 ( – 37) = 0
∴ 37[ –3(x + 2) – 4 – 3( – 1)] = 0
∴ – 3 (x + 2) – 4 + 3 = 0
∴ – 3x – 6 – 1 = 0
∴ – 3x = 7
∴ x = `-7/3`.
APPEARS IN
RELATED QUESTIONS
Using properties of determinants, prove that `|[2y,y-z-x,2y],[2z,2z,z-x-y],[x-y-z,2x,2x]|=(x+y+z)^3`
If ` f(x)=|[a,-1,0],[ax,a,-1],[ax^2,ax,a]| ` , using properties of determinants find the value of f(2x) − f(x).
By using properties of determinants, show that:
`|(a^2+1, ab, ac),(ab, b^2+1, bc),(ca, cb, c^2+1)| = 1+a^2+b^2+c^2`
Using properties of determinants, prove that:
`|(alpha, alpha^2,beta+gamma),(beta, beta^2, gamma+alpha),(gamma, gamma^2, alpha+beta)|` = (β – γ) (γ – α) (α – β) (α + β + γ)
Using properties of determinants, prove that:
`|(1, 1+p, 1+p+q),(2, 3+2p, 4+3p+2q),(3,6+3p,10+6p+3q)| = 1`
Using properties of determinants, prove that `|(x,x+y,x+2y),(x+2y, x,x+y),(x+y, x+2y, x)| = 9y^2(x + y)`
Using properties of determinants, prove that `|(1,1,1+3x),(1+3y, 1,1),(1,1+3z,1)| = 9(3xyz + xy + yz+ zx)`
Using properties of determinants show that
`[[1,1,1+x],[1,1+y,1],[1+z,1,1]] = xyz+ yz +zx+xy.`
Prove the following using properties of determinants :
\[\begin{vmatrix}a + b + 2c & a & b \\ c & b + c + 2a & b \\ c & a & c + a + 2b\end{vmatrix} = 2\left( a + b + c \right) {}^3\]
Using properties of determinants, prove that:
`|[a^2 + 1, ab, ac], [ba, b^2 + 1, bc ], [ca, cb, c^2+1]| = a^2 + b^2 + c^2 + 1`
Using properties of determinants, find the value of x for which
`|(4-"x",4+"x",4+"x"),(4+"x",4-"x",4+"x"),(4+"x",4+"x",4-"x")|= 0`
Without expanding evaluate the following determinant:
`|(1, "a", "b" + "c"),(1, "b", "c" + "a"),(1, "c", "a" + "b")|`
Without expanding the determinant, find the value of `|(10, 57, 107),(12, 64, 124),(15, 78, 153)|`.
Without expanding determinants, find the value of `|(2014, 2017, 1),(2020, 2023, 1),(2023, 2026, 1)|`
Find the value (s) of x, if `|(1, 4, 20),(1, -2, -5),(1, 2x, 5x^2)|` = 0
Without expanding evaluate the following determinant:
`|(2, 7, 65),(3, 8, 75),(5, 9, 86)|`
Select the correct option from the given alternatives:
The value of a for which system of equation a3x + (a + 1)3 y + (a + 2)3z = 0 ax + (a +1)y + (a + 2)z = 0 and x + y + z = 0 has non zero Soln. is
Select the correct option from the given alternatives:
The system 3x – y + 4z = 3, x + 2y – 3z = –2 and 6x + 5y + λz = –3 has at least one Solution when
Select the correct option from the given alternatives:
If `|(6"i", -3"i", 1),(4, 3"i", -1),(20, 3, "i")|` = x + iy then
Select the correct option from the given alternatives:
Which of the following is correct
Answer the following question:
By using properties of determinant prove that `|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)|` = 0
Answer the following question:
Without expanding determinant show that
`|(x"a", y"b", z"c"),("a"^2, "b"^2, "c"^2),(1, 1, 1)| = |(x, y, z),("a", "b", "c"),("bc", "ca", "ab")|`
Answer the following question:
Without expanding determinant show that
`|(l, "m", "n"),("e", "d", "f"),("u", "v", "w")| = |("n", "f", "w"),(l, "e", "u"),("m", "d", "v")|`
Evaluate: `|("a" - "b" - "c", 2"a", 2"a"),(2"b", "b" - "c" - "a", 2"b"),(2"c", 2"c", "c" - "a" - "b")|`
If `[(4 - x, 4 + x, 4 + x),(4 + x, 4 - x, 4 + x),(4 + x, 4 + x, 4 - x)]` = 0, then find values of x.
Let 'A' be a square matrix of order 3 × 3, then |KA| is equal to:
Let a, b, c be such that b(a + c) ≠ 0 if
`|(a, a + 1, a - 1),(-b, b + 1, b - 1),(c, c - 1, c + 1)| + |(a + 1, b + 1, c - 1),(a - 1, b - 1, c + 1),((-1)^(n + 2)a, (-1)^(n + 1)b, (-1)^n c)|` = 0, then the value of n is ______.
If `|(α, 3, 4),(1, 2, 1),(1, 4, 1)|` = 0, then the value of α is ______.
Without expanding determinants find the value of `|(10,57,107), (12, 64, 124), (15, 78, 153)|`
By using properties of determinant prove that
`|(x+ y,y+z, z+x ),(z, x,y),(1,1,1)|` = 0
By using properties of determinant prove that `|(x+y,y+z,z+x),(z,x,y),(1,1,1)|` = 0
Without expanding evaluate the following determinant:
`|(1, a, b + c), (1, b, c + a), (1, c, a + b)|`
By using properties of determinants, prove that
`|(x+y, y+z, z+x),(z, x, y),(1, 1, 1)|` = 0
Without expanding evaluate the following determinant.
`|(1,"a","b+c"),(1,"b","c+a"),(1,"c","a+b")|`
Without expanding evaluate the following determinant.
`|(1, a, b+c), (1, b, c+a), (1, c, a+b)|`
Without expanding determinants, find the value of `|(10, 57, 107),(12, 64, 124),(15, 78, 153)|`
By using properties of determinant prove that `|(x+y,y+z,z+x),(z,x,y),(1,1,1)|` = 0.
