Advertisements
Advertisements
प्रश्न
Which of the following is not correct?
पर्याय
\[|A| = | A^T |,\text{ where }A = \left[ a_{ij} \right]_{3 \times 3}\]
\[|kA| = | k^3 |,\text{ where }A = \left[ a_{ij} \right]_{3 \times 3}\]
If A is a skew-symmetric matrix of odd order, then |A| = 0
\[\begin{vmatrix}a + b & c + d \\ e + f & g + h\end{vmatrix} = \begin{vmatrix}a & c \\ e & g\end{vmatrix} + \begin{vmatrix}b & d \\ f & h\end{vmatrix}\]
Advertisements
उत्तर
(d) \[\begin{vmatrix}a + b & c + d \\ e + f & g + h\end{vmatrix} = \begin{vmatrix}a & c \\ e & g\end{vmatrix} + \begin{vmatrix}b & d \\ f & h\end{vmatrix}\]
\[\begin{vmatrix} a + b & c + d\\e + f & g + h \end{vmatrix} = \begin{vmatrix} a + b & c\\e + f & g \end{vmatrix} + \begin{vmatrix} a + b & d\\e + f & h \end{vmatrix}\]
\[ = \begin{vmatrix} a & c\\e & g \end{vmatrix} + \begin{vmatrix} b & c\\f & g \end{vmatrix} + \begin{vmatrix} a & d \\e & h \end{vmatrix} + \begin{vmatrix} b & d\\f & h \end{vmatrix}\]
APPEARS IN
संबंधित प्रश्न
If A = `[(1,1,-2),(2,1,-3),(5,4,-9)]`, find |A|.
Find the value of x, if `|(2,3),(4,5)|=|(x,3),(2x,5)|`.
Without expanding at any stage, find the value of:
`|(a,b,c),(a+2x,b+2y,c+2z),(x,y,z)|`
A matrix A of order 3 × 3 has determinant 5. What is the value of |3A|?
On expanding by first row, the value of the determinant of 3 × 3 square matrix
\[A = \left[ a_{ij} \right]\text{ is }a_{11} C_{11} + a_{12} C_{12} + a_{13} C_{13}\] , where [Cij] is the cofactor of aij in A. Write the expression for its value on expanding by second column.
If A is a 3 × 3 matrix, \[\left| A \right| \neq 0\text{ and }\left| 3A \right| = k\left| A \right|\] then write the value of k.
If A is a matrix of order 3 and |A| = 8, then |adj A| = __________ .
Using matrices, solve the following system of linear equations :
x + 2y − 3z = −4
2x + 3y + 2z = 2
3x − 3y − 4z = 11
Without expanding, show that Δ = `|("cosec"^2theta, cot^2theta, 1),(cot^2theta, "cosec"^2theta, -1),(42, 40, 2)|` = 0
The determinant ∆ = `|(sqrt(23) + sqrt(3), sqrt(5), sqrt(5)),(sqrt(15) + sqrt(46), 5, sqrt(10)),(3 + sqrt(115), sqrt(15), 5)|` is equal to ______.
The value of the determinant ∆ = `|(sin^2 23^circ, sin^2 67^circ, cos180^circ),(-sin^2 67^circ, -sin^2 23^circ, cos^2 180^circ),(cos180^circ, sin^2 23^circ, sin^2 67^circ)|` = ______.
The determinant ∆ = `|(cos(x + y), -sin(x + y), cos2y),(sinx, cosx, siny),(-cosx, sinx, cosy)|` is independent of x only.
If a1, a2, a3, ..., ar are in G.P., then prove that the determinant `|("a"_("r" + 1), "a"_("r" + 5), "a"_("r" + 9)),("a"_("r" + 7), "a"_("r" + 11), "a"_("r" + 15)),("a"_("r" + 11), "a"_("r" + 17), "a"_("r" + 21))|` is independent of r.
If a + b + c ≠ 0 and `|("a", "b","c"),("b", "c", "a"),("c", "a", "b")|` 0, then prove that a = b = c.
If x + y + z = 0, prove that `|(x"a", y"b", z"c"),(y"c", z"a", x"b"),(z"b", x"c", y"a")| = xyz|("a", "b", "c"),("c", "a", "b"),("b", "c", "a")|`
Let f(t) = `|(cos"t","t", 1),(2sin"t", "t", 2"t"),(sin"t", "t", "t")|`, then `lim_("t" - 0) ("f"("t"))/"t"^2` is equal to ______.
If f(x) = `|(0, x - "a", x - "b"),(x + "b", 0, x - "c"),(x + "b", x + "c", 0)|`, then ______.
If A = `[(2, lambda, -3),(0, 2, 5),(1, 1, 3)]`, then A–1 exists if ______.
If A is invertible matrix of order 3 × 3, then |A–1| ______.
If A is a matrix of order 3 × 3, then (A2)–1 = ______.
`|(0, xyz, x - z),(y - x, 0, y z),(z - x, z - y, 0)|` = ______.
If f(x) = `|((1 + x)^17, (1 + x)^19, (1 + x)^23),((1 + x)^23, (1 + x)^29, (1 + x)^34),((1 +x)^41, (1 +x)^43, (1 + x)^47)|` = A + Bx + Cx2 + ..., then A = ______.
`"A" = abs ((1/"a", "a"^2, "bc"),(1/"b", "b"^2, "ac"),(1/"c", "c"^2, "ab"))` is equal to ____________.
`abs ((1 + "a", "b", "c"),("a", 1 + "b", "c"),("a", "b", 1 + "c")) =` ____________
The value of the determinant `abs ((1,0,0),(2, "cos x", "sin x"),(3, "sin x", "cos x"))` is ____________.
Find the minor of the element of the second row and third column in the following determinant `[(2,-3,5),(6,0,4),(1,5,-7)]`
Find the 5th term of expansion of `(x^2 + 1/x)^10`?
For positive numbers x, y, z the numerical value of the determinant `|(1, log_x y, log_x z),(log_y x, 3, log_y z),(log_z x, log_z y, 5)|` is
Value of `|(2, 4),(-1, 2)|` is
