Question

$If space straight A equals open square brackets table row 8 0 row 4 cell negative 2 end cell row 3 6 end table close square brackets comma space straight B equals open square brackets table row 2 cell negative 2 end cell row 4 2 row cell negative 5 end cell 1 end table close square brackets$ , then find the matrix X. such that 2A + 3X = 5B.

Solution

Here
$straight A equals open square brackets table row 8 0 row 4 cell negative 2 end cell row 3 6 end table close square brackets comma space straight B equals open square brackets table row 2 cell negative 2 end cell row 4 2 row cell negative 5 end cell 1 end table close square brackets$
Now 2A + 3X = 5B 3X=-2A + 5B
$therefore space space space space space space 3 straight X equals negative 2 open square brackets table row 8 0 row 4 cell negative 2 end cell row 3 6 end table close square brackets plus 5 open square brackets table row 2 cell negative 2 end cell row 4 2 row cell negative 5 end cell 1 end table close square brackets space space space space space space space space space space space space equals space open square brackets table row cell negative 16 end cell 0 row cell negative 8 end cell 4 row cell negative 6 end cell cell negative 12 end cell end table close square brackets plus open square brackets table row 10 cell negative 10 end cell row 20 10 row cell negative 25 end cell 5 end table close square brackets equals open square brackets table row cell negative 16 plus 10 end cell cell 0 minus 10 end cell row cell 8 plus 20 end cell cell 4 plus 10 end cell row cell negative 6 minus 25 end cell cell negative 12 plus 5 end cell end table close square brackets therefore space space space 3 straight X equals open square brackets table row cell negative 6 end cell cell negative 10 end cell row 12 14 row cell negative 31 end cell cell negative 7 end cell end table close square brackets space space space space rightwards double arrow space straight X equals 1 third space open square brackets table row cell negative 6 end cell cell negative 10 end cell row 12 14 row cell negative 31 end cell cell negative 7 end cell end table close square brackets therefore space space space straight X equals open square brackets table row cell negative 2 end cell cell negative 10 over 3 end cell row 4 cell 14 over 3 end cell row cell negative 31 over 3 end cell cell negative 7 over 3 end cell end table close square brackets$

For Daily Free Study Material Join wiredfaculty

Matrices

Some More Questions From Matrices Chapter

If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction