Addition and Subtraction MCQ Quiz in తెలుగు - Objective Question with Answer for Addition and Subtraction - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

Given:

Concept:

Matrices: If two matrices are equal, then their corresponding elements must also be equal.

Calculation:

⇒

⇒

Since the matrices are equal, their corresponding elements must also be equal.

⇒ 2 + y = 5 and 2x + 2 = 8.

On solving the above equations, we get 

⇒ y = 3 and x = 3

∴ x = 3 and y = 3

A +  I = 

⇒A = 

$Given\; det(A)=-4$.

det(A)= 0⋅(0. 1 − 0. 1)−a. (2. 1−0. a)+1. (2. 1−0. a)

= - a. (2)+1. (2) =−2a + 2

Set equal to -4 -4" id="MathJax-Element-180-Frame" role="presentation" style="position: relative;" tabindex="0">−4-4 -4 $-4$

⇒ 2a + 2 =  -4 ⟹ −2a = −6 ⟹a = 3:

Also

det((a+1) adj ((a−1)A)) =2^m3ⁿ

• For a 3 × 3 Matrix, det(adj)(B) = (det(B))²
• For a scalar k det(kB) = k³det(B)

Let’s plug in values:

⇒ det((a−1) A) = (a−1)³.det(A) = (3−1)³.(−4)=2³.(−4) = 8.(−4) = −32

⇒ det(adj(a - 1)A)) = (-32)² = 1024

⇒ (a +1)³ = (3 + 1)³ = 64

⇒ det((a+1)adj((a−1)A)) = 64⋅1024 = 65536

Thus, 65536 = 2¹⁶3⁰

⇒ Then m = 16,n = 0

⇒ m + n  = 16 + 0 = 16

Calculation:

Given:

x + 2y =                     .... (1)

2x + 5y =                      .... (2)

Multiplying by 2 in the equation (1), we get

⇒ 2x + 4y =              .... (3)

Subtracting equation (3) from equation (2), we get

⇒ (2x + 5y) - (2x + 4y) = 

∴ y = 

Given : such that ...

Since, and are of order . So, will be a matrix of order

Let

From , we get

...... , ........

....... and .......

Solving and simultaneously we get

and

Then solving and simultaneously we get

and

Substituting all these values in , we get

Calculation

Here, stands for element of with row and column. Also, stands for co-factor of of matrix

So, we get and

To find the co-factor

Hence option 2 is correct

Concept:

Conditions for the subtraction of matrices:

Two matrices should be of the same order (number of rows = number of columns).

Add the corresponding element of other matrices.

Calculation:

Given:

|f(λx) - f(x)| = (λx - x)²

|f(λx) - f(x)| = x²(λ - 1)²

Concept:

• Here we have to use the multiplication properties of the matrixes.

Calculation:

Given:  A and B are square matrices of order n × n.

We know that,

(A - B)2 = (A - B) (A - B)

⇒ (A - B)2 = A2 - AB - BA + B2

∵  AB ≠ BA 

So, option 3 is correct.                              

Concept:

Conditions for the subtraction of matrices:

Two matrices should be of the same order (number of rows = number of columns).

Add the corresponding element of other matrices.

Calculation:

Given:

Concept:

Diagonal Matrix:

Any square matrix in which all the elements are zero except those in the principal diagonal is called a diagonal matrix.

i.e A = [aij]n × n is a diagonal matrix if aij = 0 for i ≠ j.

Note: If A = diag [a11, a22, a33, ....., ann] is a diagonal matrix of order n then  

Scalar Matrix:

A diagonal matrix in which all the principal diagonal elements are equal is called a scalar matrix.

Let A and B be any two matrices of same order m × n, then their sum A ± B = [aij ± bij]m × n where A = [aij]m × n and B = [bij]m × n

Calculation:

Given: A = diag [2, - 5, 9], B = diag [- 3, 7, 14] and C = diag [4, - 6, 3]

Here, we have to find the value of 2A + B - 5C

As we know that if, A = diag [a11, a22, a33, ....., ann] is a diagonal matrix of order n then  

∵  A = diag [2, - 5, 9], B = diag [- 3, 7, 14] and C = diag [4, - 6, 3]

⇒ 

⇒ 

⇒ 

Hence, 2A + B - 5C = diag [- 19, 27, 17]