If m[-3 4] + n[4 -3] = [10 -11] then 3m + 7n =?
Answers
Given :
m[-3 4] + n[4 -3] = [10 -11]
To find :
3m + 7n
Solution :
m[ -3 4 ] + n[ 4 -3 ] = [ -3m 4m ] + [ 4n -3n ]
= [ (-3m)+4n 4m+(-3n) ] = [ 10 -11 ]
• we can compare both sides,
-3m + 4n = 10 .... (1)
And
4m - 3n = -11 .... (2)
• Solving both equations
multiply equation (1) by 4 and equation (2) by 3
-12m + 14n = 40
and 12m - 9n = -33
• Add equation (1) and (2)
-12m + 14n + 12m - 9n = 40 - 33
5n = 7
n = 7/5
• Substitute value of n in equation (1)
-3m + 4×(7/5) = 10
-3m + 28/5 = 10
-15m + 28 = 50
-15m = 50 - 28
m = -22/15
• Substitute value of m and n in 3m + 7n
3(-22/15) + 7(7/5) = -22/5 + 49/5
= 27/5
• Henc, value of 3m + 7n is 27/5
Answer:
Given :
m[-3 4] + n[4 -3] = [10 -11]
To find :
3m + 7n
Solution :
m[ -3 4 ] + n[ 4 -3 ] = [ -3m 4m ] + [ 4n -3n ]
= [ (-3m)+4n 4m+(-3n) ] = [ 10 -11 ]
• we can compare both sides,
-3m + 4n = 10 .... (1)
And
4m - 3n = -11 .... (2)
• Solving both equations
multiply equation (1) by 4 and equation (2) by 3
-12m + 14n = 40
and 12m - 9n = -33
• Add equation (1) and (2)
-12m + 14n + 12m - 9n = 40 - 33
5n = 7
n = 7/5
• Substitute value of n in equation (1)
-3m + 4×(7/5) = 10
-3m + 28/5 = 10
-15m + 28 = 50
-15m = 50 - 28
m = -22/15
• Substitute value of m and n in 3m + 7n
3(-22/15) + 7(7/5) = -22/5 + 49/5
= 27/5
• Henc, value of 3m + 7n is 27/5