Advertisements
Advertisements
प्रश्न
Compute the products AB and BA whichever exists in each of the following cases:
[a, b]`[[c],[d]]`+ [a, b, c, d] `[[a],[b],[c],[d]]`
उत्तर
[a b] `[[c],[d]]`+[a b c d] `[[a],[b],[c],[d]]`
`⇒ [ac+ bd]+[a^2+b^2+c^2+d^2] `
`[a^2+b^2+c^2+d^2+ac+bd]`
APPEARS IN
संबंधित प्रश्न
Let `A = [(2,4),(3,2)] , B = [(1,3),(-2,5)], C = [(-2,5),(3,4)]`
Find AB
Compute the indicated product.
`[(1),(2),(3)] [2,3,4]`
Compute the indicated product.
`[(2,1),(3,2),(-1,1)][(1,0,1),(-1,2,1)]`
Show that AB ≠ BA in each of the following cases:
`A=[[1 3 0],[1 1 0],[4 1 0]]`And B=`[[0 1 0],[1 0 0],[0 5 1]]`
Evaluate the following:
`([[1 3],[-1 -4]]+[[3 -2],[-1 1]])[[1 3 5],[2 4 6]]`
Evaluate the following:
`[[],[1 2 3],[]]` `[[1 0 2],[2 0 1],[0 1 2]]` `[[2],[4],[6]]`
Evaluate the following:
`[[1 -1],[0 2],[2 3]]` `([[1 0 2],[2 0 1]]-[[0 1 2],[1 0 2]])`
If A = `[[1 0],[0 1]]`,B`[[1 0],[0 -1]]`
and C= `[[0 1],[1 0]]`
, then show that A2 = B2 = C2 = I2.
If A =
\[\begin{bmatrix}2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4\end{bmatrix}\]and B =
\[\begin{bmatrix}- 1 & 3 & 5 \\ 1 & - 3 & - 5 \\ - 1 & 3 & 5\end{bmatrix}\] , show that AB = BA = O3×3.
If
If f (x) = x3 + 4x2 − x, find f (A), where\[A = \begin{bmatrix}0 & 1 & 2 \\ 2 & - 3 & 0 \\ 1 & - 1 & 0\end{bmatrix}\]
Find the matrix A such that [2 1 3 ] `[[-1,0,-1],[-1,1,0],[0,1,1]] [[1],[0],[-1]]=A`
If `A=[[0,0],[4,0]]` find `A^16`
If `A=[[0,-x],[x,0]],[[0,1],[1,0]]` and `x^2=-1,` then show that `(A+B)^2=A^2+B^2`
`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= [[1,1,1],[0,1,1],[0,0,1]]` Use the principle of mathematical introduction to show that `A^n [[1,n,n(n+1)//2],[0,1,1],[0,0,1]]` for every position integer n.
A trust fund has Rs 30000 that must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs 30000 among the two types of bonds. If the trust fund must obtain an annual total interest of(ii) Rs 2000
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?
Let `A= [[1,-1,0],[2,1,3],[1,2,1]]` And `B=[[1,2,3],[2,1,3],[0,1,1]]` Find `A^T,B^T` and verify that (A + B)T = AT + BT
Let `A= [[1,-1,0],[2,1,3],[1,2,1]]` And `B=[[1,2,3],[2,1,3],[0,1,1]]` Find `A^T,B^T` and verify that (2A)T = 2AT.
Given an example of two non-zero 2 × 2 matrices A and B such that AB = O.
For any square matrix write whether AAT is symmetric or skew-symmetric.
If `[2 1 3]([-1,0,-1],[-1,1,0],[0,1,1])([1],[0],[-1])=A` , then write the order of matrix A.
If `A=[[i,0],[0,i ]]` , n ∈ N, then A4n equals
If A and B are two matrices such n that AB = B and BA = A , `A^2 + B^2` is equal to
If \[A = \begin{bmatrix}1 & a \\ 0 & 1\end{bmatrix}\]then An (where n ∈ N) equals
If \[A = \begin{bmatrix}1 & - 1 \\ 2 & - 1\end{bmatrix}, B = \begin{bmatrix}a & 1 \\ b & - 1\end{bmatrix}\]and (A + B)2 = A2 + B2, values of a and b are
The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is
The number of possible matrices of order 3 × 3 with each entry 2 or 0 is
Give an example of matrices A, B and C such that AB = AC, where A is nonzero matrix, but B ≠ C.
Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2B2? Give reasons.
Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: A(BC) = (AB)C
If A and B are square matrices of the same order, then (AB)′ = ______.
If A `= [(1,3),(3,4)]` and A2 − kA − 5I = 0, then the value of k is ______.
