If A is non-singular matrix of order 3 and ${\text{|adjA| = |A}}{{\text{|}}^{\text{K}}}$, then write the value of K.
Answer
265.9k+ views
Hint: In order to solve this problem one must know the formula ${\text{|adjA| = |A}}{{\text{|}}^{{\text{n - 1}}}}$ where n is the order of the matrix. Using this will solve our problem and we will get the right value of K.
Complete step-by-step answer:
The given equation is ${\text{|adjA| = |A}}{{\text{|}}^{\text{K}}}$ A is a matrix of order 3.
And we know that if A is a matrix of order 3 then ${\text{|adjA| = |A}}{{\text{|}}^{{\text{n - 1}}}}$ where n is the order of the matrix.
Here order is 3 so n = 3.
Then we can say that ${\text{|adjA| = |A}}{{\text{|}}^{\text{K}}}{\text{ = |A}}{{\text{|}}^{{\text{n - 1}}}} = {\text{|A}}{{\text{|}}^{3 - 1}}{\text{ = |A}}{{\text{|}}^2}$
Then we get ${\text{|A}}{{\text{|}}^{\text{K}}} = {\text{|A}}{{\text{|}}^2}$
Hence, the value of K is 2.
Note: Whenever you face such types of problems then you need to know the most important formula of matrices and determinants like ${\text{|adjA| = |A}}{{\text{|}}^{{\text{n - 1}}}}$ where n is the order of the matrix.
Complete step-by-step answer:
The given equation is ${\text{|adjA| = |A}}{{\text{|}}^{\text{K}}}$ A is a matrix of order 3.
And we know that if A is a matrix of order 3 then ${\text{|adjA| = |A}}{{\text{|}}^{{\text{n - 1}}}}$ where n is the order of the matrix.
Here order is 3 so n = 3.
Then we can say that ${\text{|adjA| = |A}}{{\text{|}}^{\text{K}}}{\text{ = |A}}{{\text{|}}^{{\text{n - 1}}}} = {\text{|A}}{{\text{|}}^{3 - 1}}{\text{ = |A}}{{\text{|}}^2}$
Then we get ${\text{|A}}{{\text{|}}^{\text{K}}} = {\text{|A}}{{\text{|}}^2}$
Hence, the value of K is 2.
Note: Whenever you face such types of problems then you need to know the most important formula of matrices and determinants like ${\text{|adjA| = |A}}{{\text{|}}^{{\text{n - 1}}}}$ where n is the order of the matrix.
Last updated date: 02nd Oct 2023
•
Total views: 265.9k
•
Views today: 5.65k
Recently Updated Pages
What is the Full Form of DNA and RNA

What are the Difference Between Acute and Chronic Disease

Difference Between Communicable and Non-Communicable

What is Nutrition Explain Diff Type of Nutrition ?

What is the Function of Digestive Enzymes

What is the Full Form of 1.DPT 2.DDT 3.BCG

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is meant by shramdaan AVoluntary contribution class 11 social science CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Is current density a scalar or a vector quantity class 12 physics JEE_Main

An alternating current can be produced by A a transformer class 12 physics CBSE

What is the value of 01+23+45+67++1617+1819+20 class 11 maths CBSE
