Answer
Verified
425.1k+ views
Hint: To solve this problem we will use the properties of determinant to expand the determinant given in the question.
Complete step-by-step answer:
Now, given determinant $\vartriangle = \left| {\begin{array}{*{20}{c}}
1&{ - 3}&4 \\
3&5&{ - 3} \\
2&{ - 5}&0
\end{array}} \right|$
Now to solve the determinant we can expand the determinant through any row or through any column. We will get the same result in both cases. We will expand the given determinant through row ${R_1}$. Expanding the determinant, we get
$ \Rightarrow $ $\vartriangle = 1\left| {\begin{array}{*{20}{c}}
5&{ - 3} \\
{ - 5}&0
\end{array}} \right| - ( - 3)\left| {\begin{array}{*{20}{c}}
3&{ - 3} \\
2&0
\end{array}} \right| + 4\left| {\begin{array}{*{20}{c}}
3&5 \\
2&{ - 5}
\end{array}} \right|$
$ \Rightarrow $ $\vartriangle = 1(0 - 15) + 3(0 + 6) + 4( - 15 - 10)$
$ \Rightarrow $ $\vartriangle = - 15 + 18 - 100$
$ \Rightarrow $ $\vartriangle = - 97$
So, the value of determinant after expanding = -97.
Note: While solving the problems related to determinant, make sure that you use proper sign convention while expanding the determinant. Signs should be proper whether you expand through row or by column, it is mandatory. Also, do calculations properly to avoid any mistake.
Complete step-by-step answer:
Now, given determinant $\vartriangle = \left| {\begin{array}{*{20}{c}}
1&{ - 3}&4 \\
3&5&{ - 3} \\
2&{ - 5}&0
\end{array}} \right|$
Now to solve the determinant we can expand the determinant through any row or through any column. We will get the same result in both cases. We will expand the given determinant through row ${R_1}$. Expanding the determinant, we get
$ \Rightarrow $ $\vartriangle = 1\left| {\begin{array}{*{20}{c}}
5&{ - 3} \\
{ - 5}&0
\end{array}} \right| - ( - 3)\left| {\begin{array}{*{20}{c}}
3&{ - 3} \\
2&0
\end{array}} \right| + 4\left| {\begin{array}{*{20}{c}}
3&5 \\
2&{ - 5}
\end{array}} \right|$
$ \Rightarrow $ $\vartriangle = 1(0 - 15) + 3(0 + 6) + 4( - 15 - 10)$
$ \Rightarrow $ $\vartriangle = - 15 + 18 - 100$
$ \Rightarrow $ $\vartriangle = - 97$
So, the value of determinant after expanding = -97.
Note: While solving the problems related to determinant, make sure that you use proper sign convention while expanding the determinant. Signs should be proper whether you expand through row or by column, it is mandatory. Also, do calculations properly to avoid any mistake.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
Using the following information to help you answer class 12 chemistry CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
Write an application to the principal requesting five class 10 english CBSE
What is the type of food and mode of feeding of the class 11 biology CBSE
Name 10 Living and Non living things class 9 biology CBSE