Advertisements
Advertisements
प्रश्न
If \[A = \begin{bmatrix}0 & 2 \\ 3 & - 4\end{bmatrix}\] and \[kA = \begin{bmatrix}0 & 3a \\ 2b & 24\end{bmatrix}\] then the values of k, a, b, are respectively
पर्याय
−6, −12, −18
−6, 4, 9
−6, −4, −9
−6, 12, 18
उत्तर
−6, −4, −9
\[Given: A = \begin{bmatrix}0 & 2 \\ 3 & - 4\end{bmatrix}\]
\[Here, \]
\[kA = \begin{bmatrix}0 & 3a \\ 2b & 24\end{bmatrix}\]
\[ \Rightarrow k\begin{bmatrix}0 & 2 \\ 3 & - 4\end{bmatrix} = \begin{bmatrix}0 & 3a \\ 2b & 24\end{bmatrix}\]
\[ \Rightarrow \begin{bmatrix}0 & 2k \\ 3k & - 4k\end{bmatrix} = \begin{bmatrix}0 & 3a \\ 2b & 24\end{bmatrix}\]
`"The corresponding elements of two equal matrices are equal ."`
\[ \Rightarrow 2k = 3a, 3k = \text{2b and - 4k} = 24 \]
\[Now, \]
\[ - 4k = 24 \]
\[ \Rightarrow k = - 6\]
\[Also, \]
\[2k = \text{3a and 3k }= 2b\]
⇒ 2(-6) = 3a and 3(-6) = 2b [using k = -6]
\[ \Rightarrow - 12 = \text{3a and - 18 }= 2b\]
\[ \therefore a = \text{- 4 and b} = - 9\]
APPEARS IN
संबंधित प्रश्न
If A = diag (2 − 59), B = diag (11 − 4) and C = diag (−6 3 4), find: A − 2B
Given the matrices
`A=[[2,1,1],[3,-1,0],[0,2,4]]` , `B=[[9,7,-1],[3,5,4],[2,1,6]]` `and C=[[2,-4,3],[1,-1,0],[9,4,5]]`
Verify that (A + B) + C = A + (B + C).
Find matrix A, if `[[1 2 -1],[0 4 9]]`
`+ A = [[9 -1 4],[-2 1 3]]`
\[A = \begin{bmatrix}2 & 3 \\ - 1 & 0\end{bmatrix}\],show that A2 − 2A + 3I2 = O
Show that the matrix \[A = \begin{bmatrix}2 & 3 \\ 1 & 2\end{bmatrix}\]satisfies the equation A3 − 4A2 + A = O
If `[x 2] [[3],[4]] = 2` , find x
If \[\begin{bmatrix}9 & - 1 & 4 \\ - 2 & 1 & 3\end{bmatrix} = A + \begin{bmatrix}1 & 2 & - 1 \\ 0 & 4 & 9\end{bmatrix}\] , then find matrix A.
If \[\begin{bmatrix}a - b & 2a + c \\ 2a - b & 3c + d\end{bmatrix} = \begin{bmatrix}- 1 & 5 \\ 0 & 13\end{bmatrix}\] , find the value of b.
If matrix \[A = \begin{bmatrix}2 & - 2 \\ - 2 & 2\end{bmatrix}\] and A2 = pA, then write the value of p.
If \[\begin{bmatrix}a + 4 & 3b \\ 8 & - 6\end{bmatrix} = \begin{bmatrix}2a + 2 & b + 2 \\ 8 & a - 8b\end{bmatrix}\] , write the value of a − 2b.
Find matrix X so that `x ((1,2,3),(4,5,6)) = ((-7,-8,-9),(2,4,6))`.
If \[A = \begin{bmatrix}2 & - 1 \\ - 1 & 2\end{bmatrix}\] and I is the identity matrix of order 2, then show that A2= 4 A − 3 I. Hence find A−1.
If \[A = \begin{bmatrix}1 & - 1 \\ 2 & - 1\end{bmatrix} \text { and } B = \begin{bmatrix}a & 1 \\ b & - 1\end{bmatrix} \text { and } \left( A + B \right)^2 = A^2 + B^2\] , then find the values of a and b.
Matrix subtraction is associative
If A = `[(1, 2),(-2, 1)]`, B = `[(2, 3),(3, -4)]` and C = `[(1, 0),(-1, 0)]`, verify: (AB)C = A(BC)
If A = `[(1, 2),(4, 1),(5, 6)]` B = `[(1, 2),(6, 4),(7, 3)]`, then verify that: (A – B)′ = A′ – B′
Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: a(C – A) = aC – aA
Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: (A – B)C = AC – BC
Matrices of different orders can not be subtracted.
If A and B are two matrices of the same order, then A – B = B – A.
If A `= [(2,2,1),(1,3,1),(1,2,2)], "then" "A"^4 - 2 ^4` (A - I) = ____________.
