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1.
If P = $open square brackets table row 1 straight alpha 3 row 1 3 3 row 2 4 4 end table close square brackets$ is the adjoint of a 3 x3 matrix A and |A| = 4, then α is equal to

4

11

5

5

Given,
$straight P space equals space open square brackets table row 1 straight alpha 3 row 1 3 3 row 2 4 4 end table close square brackets$
|P| = 1(12-12)-α (4-6) +3(4-6)
= 2α -6.
∵ P =adj(A)
∴ |P| = |adj A | = |A|3-1 = |A|2 = 16
[∵ |adj A| = |A|n-1 order is 3 x3
∴ 2α -6 = 16
2α = 22
α = 11

547 Views

Let A = $open square brackets table row 1 0 0 row 2 1 0 row 3 2 1 end table close square brackets$ . If u₁ and u₂ are column matrices such that Au1 = $open square brackets table row 1 row 0 row 0 end table close square brackets$ and Au2 = $open square brackets table row 0 row 1 row 0 end table close square brackets$ , then u₁ +u₂ is equal to

$open square brackets table row cell negative 1 end cell row 1 row 0 end table close square brackets$
$open square brackets table row cell negative 1 end cell row cell space space space 1 end cell row cell negative 1 end cell end table close square brackets$
$open square brackets table row cell negative 1 end cell row cell negative 1 end cell row 0 end table close square brackets$
$open square brackets table row cell negative 1 end cell row cell negative 1 end cell row 0 end table close square brackets$

480 Views

Let A and B be two symmetric matrices of order 3.
Statement-1: A(BA) and (AB)A are symmetric matrices.
Statement-2: AB is symmetric matrix if matrix multiplication of A with B is commutative.

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Statement-1 is true, Statement-2 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
Statement-1 is true, Statement-2 is false.
Statement-1 is true, Statement-2 is false.

191 Views

The number of 3 × 3 non-singular matrices, with four entries as 1 and all other entries as 0, is

less than 4
5
6
6

178 Views

Let f : R → R be defined by
$straight f left parenthesis straight x right parenthesis space equals space open curly brackets table attributes columnalign left end attributes row cell straight k minus 2 straight x comma if space straight x space less or equal than space minus 1 end cell row cell 2 straight x space plus 3 comma space if space straight x greater than negative 1 end cell end table close$
If f has a local minimum at x = - 1 then a possible value of k is

1
0
-1/2
-1/2

137 Views

If S is the set of distinct values of 'b' for which the following system of linear equations
x + y + z = 1
x + ay + z = 1
ax + by + z = 0
has no solution, then S is

a singleton
an empty set
an infinite set
an infinite set

297 Views

Let ω be a complex number such that 2ω +1 = z where z = √-3. if

$open vertical bar table row 1 1 1 row 1 cell negative straight omega squared end cell cell straight omega squared end cell row 1 cell straight omega squared end cell cell straight omega to the power of 7 end cell end table close vertical bar space equals space 3 straight k$
then k is equal to

1
-z
z
z

307 Views

Let a, b, c be such that 0 (a +c) ≠ . If $open vertical bar table row cell space space space straight a end cell cell straight a plus 1 end cell cell space space straight a minus 1 end cell row cell negative straight b end cell cell straight b plus 1 end cell cell space space straight b minus 1 end cell row cell space space space straight c end cell cell space straight c minus 1 end cell cell space space straight c plus 1 end cell end table close vertical bar plus open vertical bar table row cell straight a plus 1 end cell cell straight b plus 1 end cell blank row cell straight a minus 1 end cell cell straight b minus 1 end cell cell straight c plus 1 end cell row cell left parenthesis negative 1 right parenthesis to the power of straight n plus 2 end exponent straight a end cell cell left parenthesis negative 1 right parenthesis to the power of straight n plus 1 end exponent straight b end cell cell left parenthesis negative 1 right parenthesis to the power of straight n space straight c end cell end table close vertical bar space equals space 0$ ,then the value of 'n' is

0
any even integer
any odd integer
any odd integer

167 Views

Let A be a 2 × 2 matrix
Statement 1 : adj (adj A) = A
Statement 2 : |adj A| = |A|

Statement–1 is true, Statement–2 is true, Statement–2 is a correct explanation for statement–1
Statement–1 is true, Statement–2 is true; Statement–2 is not a correct explanation for statement–1.
Statement–1 is true, statement–2 is false.
Statement–1 is true, statement–2 is false.

178 Views