Question

if the value of the determinant is m upon - 5 and 6 upon 4 is 58 then m=​

Answer 1

Question:

If the value of the determinant $\displaystyle{\left|\begin{array}{cc}\sf\:m & \sf\:6\\\sf\:-\:5 & \sf\:4\end{array}\right|}$ is 58, then find the value of m.

Answer:

The value of m is 7.

Step-by-step-explanation:

The given determinant is

$\displaystyle{\left|\begin{array}{cc}\sf\:m & \sf\:6\\\sf\:-\:5 & \sf\:4\end{array}\right|\sf\:=\:58}$

Now,

$\displaystyle{\left|\begin{array}{cc}\sf\:m & \sf\:6\\\sf\:-\:5 & \sf\:4\end{array}\right|\sf\:=\:58}$

$\displaystyle{\implies\sf\:m\:\times\:4\:-\:\left[\:6\:\times\:(\:-\:5\:)\:\right]\:=\:58}$

$\displaystyle{\implies\sf\:4m\:-\:\left(\:-\:30\:\right)\:=\:58}$

$\displaystyle{\implies\sf\:4m\:+\:30\:=\:58}$

$\displaystyle{\implies\sf\:4m\:=\:58\:-\:30}$

$\displaystyle{\implies\sf\:4m\:=\:28}$

$\displaystyle{\implies\sf\:m\:=\:\cancel{\dfrac{28}{4}}}$

$\displaystyle{\implies\boxed{\red{\sf\:m\:=\:7}}}$

The value of m is 7.

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Additional Information:

1. Determinant:

A structure of some numbers or elements between two straight lines is called as a determinant.

2. It is denoted using vertical pipe symbol ( | ).

3. If a, b, c and d are the elements of a determinant with its value x, it can be shown as:

$\displaystyle{\left|\begin{array}{cc}\sf\:a & \sf\:b\\\sf\:c & \sf\:d\end{array}\right|\sf\:=\:x}$

4. To solve this determinant, we have to subtract the product of b and c from the product of a and d.

$\displaystyle{\sf\:(\:a\:\times\:d\:)\:-\:(\:b\:\times\:c\:)\:=\:x}$

5. Linear equations in two variables can be solved using Cramer's rule which is based on determinants.

Answer 2

Answer:

Step-by-step explanation:

$ANSWER∣∣∣∣∣∣​ m−5​ 64​ ∣∣∣∣∣∣​ = 58=4m−(÷30)=58=4m=58−30=28∴m=7$