Class interval 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 8 5 12 35 24 16 Solution: Class mark, xi = (upper class limit + lower class limit)/2 Class interval Frequency fi Class mark xi fixi 0-10 8...
If A=
and B=
Find(iii) BA
If A=
and B=
Find (i)
(ii)
Find a and b if
On comparing the corresponding terms, we have \[\begin{array}{*{35}{l}} 2a\text{ }\text{ }4\text{ }=\text{ }0 \\ 2a\text{ }=\text{ }4 \\ a\text{ }=\text{ }4/2 \\ a\text{ }=\text{ }2 \\...
If
find a, b, c and d.
Given, On comparing the corresponding elements, we have \[\begin{array}{*{35}{l}} -a\text{ }=\text{ }1\Rightarrow a\text{ }=\text{ }-1 \\ -b\text{ }=\text{ }0\Rightarrow b\text{ }=\text{ }0 \\...
If A=
and
, find p and q.
On comparing the corresponding elements, we have \[\begin{array}{*{35}{l}} 9\text{ }+\text{ }3p\text{ }=\text{ }0 \\ 3p\text{ }=\text{ }-9 \\ p\text{ }=\text{ }-9/3 \\ p\text{ }=\text{...
If A=
, find
, where I is unit matrix of order
.
Given,
If A=
and B=
, find the each of the following and state it they are equal: (i) (A + B) (A – B) (ii)
Given, Hence, its clearly seen that \[\left( A\text{ }+\text{ }B \right)\text{ }\left( A\text{ }\text{ }B \right)\text{ }\ne \text{ }{{A}^{2}}~\text{ }{{B}^{2}}\].
(i) Find the matrix B if A=
and
(ii) If A=
, B=
and C=
find
Comparing the corresponding elements, we have \[\begin{array}{*{35}{l}} 4\text{ }+\text{ }2a\text{ }=\text{ }18 \\ 2a\text{ }=\text{ }18\text{ }\text{ }4\text{ }=\text{ }14 \\ a\text{...
Determine the matrices A and B when
and
Given,
Find a, b, c and d if
Given \[3\left[ \begin{align} & a\,\,\,\,\,\,b \\ & c\,\,\,\,\,\,\,d \\ \end{align} \right]=\left[ \begin{align} & 4\,\,\,\,\,\,\,\,\,\,a+b \\ & c+d\,\,\,\,\,\,\,3 \\ \end{align}...
Find the values of a and b if
Given \[\left[ \begin{align} & a+3\,\,\,\,\,\,\,{{b}^{2}}+2 \\ & \,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-6 \\ \end{align} \right]=\left[ \begin{align} & 2a+1\,\,\,\,\,\,\,\,\,\,\,\,3b \\...
Find the values of x and y if
Given, On comparing the corresponding elements, we have \[2x\text{ }+\text{ }y\text{ }=\text{ }3\]… (i) \[3x\text{ }+\text{ }y\text{ }=\text{ }2\]… (ii) Subtracting, we get \[-x\text{ }=\text{...
.(i) Find x and y if
(ii) Find x and y if
Comparing the corresponding elements, \[\begin{array}{*{35}{l}} \text{ }3x\text{ }+\text{ }4\text{ }=\text{ }-5 \\ -3x\text{ }=\text{ }-5\text{ }\text{ }4\text{ }=\text{ }-9 \\ x\text{ }=\text{...
If A =
find the value of x, so that
Given, On comparing, \[\begin{array}{*{35}{l}} 1\text{ }+\text{ }x\text{ }=\text{ }0 \\ \therefore x\text{ }=\text{ }-1 \\ \end{array}\]
Find the matrix
which satisfies the equation
Given
Show that is a solution of the matrix equation
, where I is the unit matrix of order
.
Given,
If X=
show that
where I is the unit matrix.
Given, – Hence proved
If A=
find
and
. Also state that which of these is equal to A.
Given, From above, its clearly seen that \[{{A}^{3}}~=\text{ }A\].
If A=
B=
and C=
, find
.
Let A=
and B=
C=
find
.
Let A=
and B=
Find
.
Given,
If A=
and B=
C=
Find the matrix C(B – A).
If A=
and B=
, C=
compute (i) A(B + C) (ii) (B + C)A
If A=
and B=
find
If A=
, B=
find the matrix AB+BA
Evaluate
Given
1. Given matrices:
and
Find the products of (i) ABC (ii) ACB and state whether they are equal.
Now consider,
If
find A(BA)
If A=
B=
and C=
find
1. If A=
, B=
, find AB and BA, IS AB=BA?
1. If A=
and B=
, is the product AB possible? Give a reason. If yes, find AB
Yes, the product is possible because of number of column in A = number of row in B That is order of matrix is \[2\text{ }\times \text{ }1\]
IF A=
and B=
, C=
and
, find the values of a, b and c.
On comparing the corresponding terms, we get \[\begin{array}{*{35}{l}} 5a\text{ }+\text{ }6\text{ }=\text{ }9 \\ 5a\text{ }=\text{ }9\text{ }\text{ }6 \\ 5a\text{ }=\text{ }3 \\ a\text{ }=\text{...
If
Find the value of a, b and c.
Next, on comparing the corresponding terms, we have \[\begin{array}{*{35}{l}} a\text{ }+\text{ }1\text{ }=\text{ }5\Rightarrow a\text{ }=\text{ }4 \\ b\text{ }+\text{ }2\text{ }=\text{...
If
Find the values of x and y
Now, comparing the corresponding terms, we get \[\begin{array}{*{35}{l}} 4\text{ }\text{ }4x\text{ }=\text{ }-8 \\ 4\text{ }+\text{ }8\text{ }=\text{ }4x \\ 12\text{ }=\text{ }4x \\ x\text{...
IF
Find the values of x and y
On comparing the corresponding terms, we have \[\begin{array}{*{35}{l}} 2x\text{ }+\text{ }1\text{ }=\text{ }5 \\ 2x\text{ }=\text{ }5\text{ }-1\text{ }=\text{ }4 \\ x\text{ }=\text{ }4/2\text{...
If
Find the values of x and y
On comparing the corresponding elements, we have \[\begin{array}{*{35}{l}} 8\text{ }+\text{ }y\text{ }=\text{ }0 \\ Then,\text{ }y\text{ }=\text{ }-8 \\ And,\text{ }2x\text{ }+\text{ }1\text{...
Find X and Y if X+Y =
and X-Y=
Given
and
,
find the matrix X such that
If
, find the matrix M
Solve the matrix equation
Given \[\left[ \begin{align} & 2\,\,\,\,\,\,\,1 \\ & 5\,\,\,\,\,\,0 \\ \end{align} \right]-3X=\left[ \begin{align} & -7\,\,\,\,\,\,\,4 \\ & 2\,\,\,\,\,\,\,\,\,\,6 \\ \end{align}...
If
and
Find the matrix X if: (i)
(ii)
and
,
Find
Simplify
Given,
If A=
and B =
find
1. Given that M=
and N=
, find M+2N
Find the values of a, b, c and d if
Given \[\left[ \begin{align} & a+b\,\,\,\,\,3 \\ & 5+c\,\,\,\,\,ab \\ \end{align} \right]=\left[ \begin{align} & 6\,\,\,\,d \\ & -1\,\,\,8 \\ \end{align} \right]\] Comparing the...
Find the values of x, y and z if
Given \[\left[ \begin{align} & x+2\,\,\,\,\,\,\,\,6 \\ & 3\,\,\,\,\,\,\,\,\,\,\,\,\,\,5z \\ \end{align} \right]=\left[ \begin{align} & -5\,\,\,\,\,\,{{y}^{2}}+y \\ &...
If
Find the values of x and y.
Given \[\left[ \begin{align} & x+3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4 \\ & y-4\,\,\,\,\,\,\,\,\,\,\,\,\,\,x+y \\ \end{align} \right]=\left[ \begin{align} & 5\,\,\,\,4 \\ & 3\,\,\,\,9 \\...
Find the value of x if
Given \[\left[ \begin{align} & 3x+y\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-y \\ & 2y-x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3 \\ \end{align} \right]=\left[ \begin{align} & 1\,\,\,\,\,2 \\ &...
Find the values of x and y if:
Given \[\left[ \begin{align} & 2x+y \\ & 3x-2y \\ \end{align} \right]=\left[ \begin{align} & 5 \\ & 4 \\ \end{align} \right]\] Now by comparing the corresponding elements, \[2x\text{...
Construct a
matrix whose elements aij are given by (i)
(ii)
(i) Given \[{{\mathbf{a}}_{\mathbf{ij}}}~=\text{ }\mathbf{2i}\text{ }\text{ }\mathbf{j}\] Therefore matrix of order \[\mathbf{2}\text{ }\times \text{ }\mathbf{2}\]is \[\left[ \begin{align} &...
(i)If a matrix has
elements, what are the possible order it can have? (ii) If a matrix has
elements, what are the possible orders it can have?
It can have \[1\text{ }\times \text{ }4,\text{ }4\text{ }\times \text{ }1\text{ }or\text{ }2\text{ }\times \text{ }2\] order. (ii) If a matrix has \[4\] elements, what are the possible orders it can...
Classify the following matrices: (v)
(vi)
It is a matrix of order \[2\text{ }\times \text{ }3\] (vi) \[\left[ \begin{align} & 0\,\,\,\,\,\,\,\,0\,\,\,\,\,\,0\, \\ & 0\,\,\,\,\,\,\,\,0\,\,\,\,\,\,0 \\ \end{align} \right]\] Solution:...
Classify the following matrices: (iii)
(iv)
It is column matrix of order \[3\text{ }\times \text{ }1\] (iv) \[\left( \begin{align} & 2\,\,\,-4 \\ & 0\,\,\,\,\,\,0 \\ & 1\,\,\,\,\,\,\,7 \\ \end{align} \right)\] Solution: It is a...
Classify the following matrices: (i)
(ii)
It is square matrix of order \[2\] (ii)\[[2,3,-7]\] Solution: It is row matrix of order \[1\text{ }\times \text{ }3\]