Evaluate $\left|\begin{array}{rr}2 & 4 \\ -1 & 2\end{array}\right|$.

Step 1: Identify the determinant formula for a 2x2 matrix

To evaluate a $2 \times 2$ determinant, we use a specific formula. If the matrix is given as $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$, its determinant is calculated by multiplying the elements on the main diagonal ($a \times d$) and subtracting the product of the elements on the anti-diagonal ($b \times c$).

Step 2: Identify the elements of the given matrix

From the given determinant $\left|\begin{array}{rr}2 & 4 \\ -1 & 2\end{array}\right|$, we can identify the values of $a, b, c,$ and $d$. Here, $a=2$, $b=4$, $c=-1$, and $d=2$.

Step 3: Substitute the values into the formula

Now, substitute the identified values of $a, b, c,$ and $d$ into the determinant formula $ad - bc$. This gives us $(2)(2) - (4)(-1)$.

Step 4: Calculate the products

Perform the multiplications: $2 \times 2 = 4$ and $4 \times (-1) = -4$. So the expression becomes $4 - (-4)$.

Step 5: Simplify the expression

Subtracting a negative number is equivalent to adding its positive counterpart. Therefore, $4 - (-4)$ simplifies to $4 + 4$, which equals $8$.

More from this chapter

• Evaluate the determinant 1 & 0 & 4 3 & 5 & -1 0 & 1 & 2 (i) with the help of second row. (ii) with the help of third column.
• If A = [[1, 2], [3, 4]] find det(A) and adj(A).
• The value of 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 is:
• Using Cramer's rule, show that the following system of linear equations is consistent and hence solve it: x + y + z = 1, 2x + 3y + 2z = 2, x + y + 2z = 4.
• Let a R and A be a matrix of order 3 3 such that det(A)=-4 and A+I= 1 & a & 1 2 & 1 & 0 a & 1 & 2, where I is the 3 3 identity. If det ((a+1)adj((a-1)A))=2^m3^n
• Let A be a 3 × 3 matrix such that |adj (adj(adj A))| = 81. If S = n Z: |adj(adj A)|^(((n-1)²)/(2)) = |A|³n² - 5n - 4, then Σ_n S | A^(n² + n) | is equal to:
• Find the equation of the line joining A(1,3) and B(0,0) using determinants and find k if D(k, 0) is a point such that area of triangle ABD is 3 sq units.
• If the system of linear equations 3x + y + β z = 3, 2x + α y - z = -3, x + 2y + z = 4 has infinitely many solutions, then the value of 22β - 9α is:

All Determinants solutions →