Evaluate the determinant
Find the matrix inverse
Find the matrix transpose
Topics
Pre Calculus
Calculus
Trigonometry
\left[ \begin{array}{l} {4}&{5} \\ {-3}&{2} \end{array} \right] =
Question
\left[\begin{array}{rr}{4}&{5}\\{-3}&{2}\end{array}\right]
Matrices
Evaluate the determinant
23
Evaluate
\left[\begin{array}{rr}{4}&{5}\\{-3}&{2}\end{array}\right]
To evaluate the determinant of the matrix,use the appropriate notation
\left|\begin{array}{cc}{4}&{5}\\{-3}&{2}\end{array}\right|
Evaluate
\left[\begin{array}{rr}{4}&{5}\\{-3}&{2}\end{array}\right]
\text{Evaluate the determinant using the formula }\left| \begin{array} { l l l } { a } & { b } \\ { c } & { d } \end{array} \right| = ad - bc
4\times 2-5\left(-3\right)
Calculate the product
8-5\left(-3\right)
Calculate the product
8-\left(-15\right)
Solution
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Evaluate
8-\left(-15\right)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
8+15
Add the numbers
23
23
Find the matrix inverse
\left[\begin{array}{rr}{\frac{2}{23}}&{-\frac{5}{23}}\\{\frac{3}{23}}&{\frac{4}{23}}\end{array}\right]
Evaluate
\left[\begin{array}{rr}{4}&{5}\\{-3}&{2}\end{array}\right]
Evaluate the determinant
23
\text{Since the determinant is not 0,substitute a=}4\text{,b=}5\text{,c=}-3\text{ and d=}2\text{ into the formula for the inverse, }\frac{1}{ad-bc}\left[ \begin{array} { r r r } { d } & { -b } \\ {- c } & { a } \end{array} \right]
\frac{1}{4\times 2-5\left(-3\right)}\times \left[\begin{array}{rr}{2}&{-5}\\{3}&{4}\end{array}\right]
Evaluate
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Evaluate
4\times 2-5\left(-3\right)
Multiply the terms
8-5\left(-3\right)
Multiply the terms
8-\left(-15\right)
Evaluate
23
\frac{1}{23}\times \left[\begin{array}{rr}{2}&{-5}\\{3}&{4}\end{array}\right]
Solution
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Evaluate
\frac{1}{23}\times \left[\begin{array}{rr}{2}&{-5}\\{3}&{4}\end{array}\right]
Multiply the terms
\left[\begin{array}{rr}{\frac{1}{23}\times 2}&{\frac{1}{23}\times \left(-5\right)}\\{\frac{1}{23}\times 3}&{\frac{1}{23}\times 4}\end{array}\right]
Evaluate
\left[\begin{array}{rr}{\frac{2}{23}}&{\frac{1}{23}\times \left(-5\right)}\\{\frac{1}{23}\times 3}&{\frac{1}{23}\times 4}\end{array}\right]
Evaluate
\left[\begin{array}{rr}{\frac{2}{23}}&{-\frac{5}{23}}\\{\frac{1}{23}\times 3}&{\frac{1}{23}\times 4}\end{array}\right]
Evaluate
\left[\begin{array}{rr}{\frac{2}{23}}&{-\frac{5}{23}}\\{\frac{3}{23}}&{\frac{1}{23}\times 4}\end{array}\right]
Evaluate
\left[\begin{array}{rr}{\frac{2}{23}}&{-\frac{5}{23}}\\{\frac{3}{23}}&{\frac{4}{23}}\end{array}\right]
\left[\begin{array}{rr}{\frac{2}{23}}&{-\frac{5}{23}}\\{\frac{3}{23}}&{\frac{4}{23}}\end{array}\right]
Find the matrix transpose
\left[\begin{array}{rr}{4}&{-3}\\{5}&{2}\end{array}\right]
Evaluate
\left[\begin{array}{rr}{4}&{5}\\{-3}&{2}\end{array}\right]
Solution
\left[\begin{array}{rr}{4}&{-3}\\{5}&{2}\end{array}\right]
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