Advertisements
Advertisements
प्रश्न
If A = `[(3, 5)]`, B = `[(7, 3)]`, then find a non-zero matrix C such that AC = BC.
उत्तर
We have, A = `[(3, 5)]_(1 xx 2)` and B = `[(7, 3)]_(1 xx 2)`
For AC = BC
We have order of C = 2 × n
For n = 1
Let C = `[(x),(y)]`
∴ AC = `[(3, 5)] [(x),(y)] = [(3x + 5y]`
And BC = `[(7, 3)] [(x),(y)]` = [3x + 5y]
For AC = BC,
[3x + 5y] = [7x + 3y]
⇒ 3x + 5y = 7x + 3y
⇒ 4x = 2y
⇒ x = `1/2 y`
⇒ y = 2x
∴ C = `[(x),(2x)]`
We see that on taking C of order 2 × 1, 2 × 2, 2 × 3, ..., we get
C = `[(x),(2x)], [(x, x),(2x, 2x)], [(x, x, x),(2x, 2x, 2x)]`...
In general,
C = `[("k"),(2"k")], [("k", "k"),(2"k", 2"k")]` etc ...
Where, k is any real number.
APPEARS IN
संबंधित प्रश्न
Compute the indicated products
`[(2,3,4),(3,4,5),(4,5,6)][(1,-3,5),(0,2,4), (3,0,5)]`
Show that AB ≠ BA in each of the following cases:
`A = [[1,3,-1],[2,-1,-1],[3,0,-1]]` And `B= [[-2,3,-1],[-1,2,-1],[-6,9,-4]]`
\[A = \begin{bmatrix}3 & 1 \\ - 1 & 2\end{bmatrix} and \text{ I} = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\]
If [1 1 x] `[[1 0 2],[0 2 1],[2 1 0]] [[1],[1],[1]]` = 0, find x.
Solve the matrix equations:
`[1 2 1] [[1,2,0],[2,0,1],[1,0 ,2]][[0],[2],[x]]=0`
If f (x) = x2 − 2x, find f (A), where A=
`A=[[1,2,2],[2,1,2],[2,2,1]]`, then prove that A2 − 4A − 5I = 0
`A=[[3,2, 0],[1,4,0],[0,0,5]]` show that A2 − 7A + 10I3 = 0
`A=[[1,0,-3],[2,1,3],[0,1,1]]`then verify that A2 + A = A(A + I), where I is the identity matrix.
Let A and B be square matrices of the same order. Does (A + B)2 = A2 + 2AB + B2 hold? If not, why?
There are 2 families A and B. There are 4 men, 6 women and 2 children in family A, and 2 men, 2 women and 4 children in family B. The recommend daily amount of calories is 2400 for men, 1900 for women, 1800 for children and 45 grams of proteins for men, 55 grams for women and 33 grams for children. Represent the above information using matrix. Using matrix multiplication, calculate the total requirement of calories and proteins for each of the two families. What awareness can you create among people about the planned diet from this question?
A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received ₹ 2800 as interest. However, if trust had interchanged money in bonds, they would have got ₹ 100 less as interes. Using matrix method, find the amount invested by the trust.
If \[A = \begin{bmatrix}1 \\ 2 \\ 3\end{bmatrix}\] write AAT.
For any square matrix write whether AAT is symmetric or skew-symmetric.
Let A = \[\begin{bmatrix}a & 0 & 0 \\ 0 & a & 0 \\ 0 & 0 & a\end{bmatrix}\], then An is equal to
If A = [aij] is a scalar matrix of order n × n such that aii = k, for all i, then trace of A is equal to
If \[A = \begin{bmatrix}2 & - 1 & 3 \\ - 4 & 5 & 1\end{bmatrix}\text{ and B }= \begin{bmatrix}2 & 3 \\ 4 & - 2 \\ 1 & 5\end{bmatrix}\] then
If A = `[[3,9,0] ,[1,8,-2], [7,5,4]]` and B =`[[4,0,2],[7,1,4],[2,2,6]]` , then find the matrix `B'A'` .
If A = `[(2, -1, 3),(-4, 5, 1)]` and B = `[(2, 3),(4, -2),(1, 5)]`, then ______.
If X = `[(3, 1, -1),(5, -2, -3)]` and Y = `[(2, 1, -1),(7, 2, 4)]`, find 2X – 3Y
If X = `[(3, 1, -1),(5, -2, -3)]` and Y = `[(2, 1, -1),(7, 2, 4)]`, find A matrix Z such that X + Y + Z is a zero matrix
If A = `[(0, 1),(1, 0)]`, then A2 is equal to ______.
A matrix which is not a square matrix is called a ______ matrix.
If matrix AB = O, then A = O or B = O or both A and B are null matrices.
If A `= [(1,3),(3,4)]` and A2 − kA − 5I = 0, then the value of k is ______.
If A = `[(1, 1, 1),(0, 1, 1),(0, 0, 1)]` and M = A + A2 + A3 + .... + A20, then the sum of all the elements of the matrix M is equal to ______.
