Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Matrices

Short Answer Type

111.

If space straight A equals space open square brackets table row 3 cell negative 4 end cell row cell negative 1 end cell cell space space space space 2 end cell end table close square brackets space find space straight a space matrix space straight B space such space that space AB space equals space straight I.

89 Views

112. Find a 2 X 2 matrix B such that

open square brackets table row 2 5 row cell negative 3 end cell 7 end table close square brackets space space straight B equals open square brackets table row 17 cell negative 1 end cell row 47 cell negative 13 end cell end table close square brackets

75 Views

113. Without using'the concept of inverse of a matrix, find the matrix

open square brackets table row straight x straight y row straight z straight u end table close square brackets

such that

open square brackets table row 5 cell negative 7 end cell row cell negative 2 end cell 3 end table close square brackets space open square brackets table row x y row z u end table close square brackets equals space open square brackets table row cell negative 16 end cell cell negative 6 end cell row 7 2 end table close square brackets

70 Views

114. $Find space the space matrix space x space so space that space x space space open square brackets table row 1 2 3 row 4 5 6 end table close square brackets equals space open square brackets table row cell negative 7 end cell cell negative 8 end cell cell negative 9 end cell row 2 4 6 end table close square brackets$

$space We space are space given space that x space open square brackets table row 1 2 3 row 4 5 6 end table close square brackets equals open square brackets table row cell negative 7 end cell cell negative 8 end cell cell negative 9 end cell row 2 4 6 end table close square brackets Where space x space is space straight a space matrix.$
Let x be of m X n type.
Since number of columns of x = number of rows of
$open square brackets table row 1 2 3 row 4 5 6 end table close square brackets therefore space straight n equals 2 open square brackets table row 1 2 3 row 4 5 6 end table close square brackets space is space space of space 2 space straight x space 3 space type x space open square brackets table row 1 2 3 row 4 5 6 end table close square brackets space space must space be space of space type space straight m space straight X space 3. therefore space straight m equals 2 therefore space straight X space is space straight a space square space matrix space of space type space 2 straight x 2. Let space space space space space space space space space straight X equals open square brackets table row straight a straight b row straight c straight d end table close square brackets Now space straight X space open square brackets table row 1 2 3 row 4 5 6 end table close square brackets equals open square brackets table row cell negative 7 end cell cell negative 8 end cell cell negative 9 end cell row cell negative 2 end cell 4 6 end table close square brackets rightwards double arrow open square brackets table row straight a straight b row straight c straight d end table close square brackets space open square brackets table row 1 2 3 row 4 5 6 end table close square brackets equals open square brackets table row cell negative 7 end cell cell negative 8 end cell cell negative 9 end cell row cell negative 2 end cell 4 6 end table close square brackets rightwards double arrow open square brackets table row cell straight a plus 4 straight b end cell cell 2 straight a plus 5 straight b end cell cell 3 straight a plus 6 straight b end cell row cell straight c plus 4 straight d end cell cell 2 straight c plus 5 straight d end cell cell 3 straight c plus 6 straight d end cell end table close square brackets equals open square brackets table row cell negative 7 end cell cell negative 8 end cell cell negative 9 end cell row cell negative 2 end cell 4 6 end table close square brackets$

By the definition of equality of matrices,
a + 4b = –7    ...(1)
2a + 5 b =–8    ..(2)
3a + 6 b = –9    –(3)
c + 4 d = 2 ......(4)
2c + 5 d = 4        (5)
3 c + 6 d = 6    ....(6)
Multiplying (1) by 2 and (2) by 1, we get,
2a + 8 b = –14    ...(7)
2a + 5 b = –8     .(8)
Subtracting (8) from (7), we get,
3b = –6 or b = – 2
∴ from (1), a - 8 = – 7 or a = 1
Now a = 1, b = -2 also satisfy (3)
∴ we have a= 1, b = – 2
Multiplying (4) by 2 and (5) by 1, we get
2 c + 8 d = 4    (9)
2;c + 5 d = 4    ...(10)
Subtracting (10) from (9), we get
3d = 0 or d = 0
∴from (4), c + 0 = 2 or c = 2
Now c = 2, d = 0 satisfy (6)