If A = [[2, 3], [1, 4]], what is the inverse of A?

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Question: If A = [[2, 3], [1, 4]], what is the inverse of A?

Options:

[[4, -3], [-1, 2]]
[[4, 3], [-1, 2]]
[[2, -3], [-1, 2]]
[[3, -2], [-1, 2]]

Correct Answer: [[4, -3], [-1, 2]]

Solution:

The inverse of A is given by (1/det(A)) * adj(A). Det(A) = (2*4) - (3*1) = 5. The adjoint is [[4, -3], [-1, 2]]. Thus, A^(-1) = (1/5) * [[4, -3], [-1, 2]].

If A = [[2, 3], [1, 4]], what is the inverse of A?

Practice Questions

If A = [[2, 3], [1, 4]], what is the inverse of A?

[[4, -3], [-1, 2]]
[[4, 3], [-1, 2]]
[[2, -3], [-1, 2]]
[[3, -2], [-1, 2]]

Questions & Step-by-Step Solutions

If A = [[2, 3], [1, 4]], what is the inverse of A?

Step 1: Identify the matrix A. Here, A = [[2, 3], [1, 4]].
Step 2: Calculate the determinant of A. Use the formula det(A) = (a*d) - (b*c), where A = [[a, b], [c, d]]. For our matrix, a = 2, b = 3, c = 1, d = 4. So, det(A) = (2*4) - (3*1) = 8 - 3 = 5.
Step 3: Find the adjoint (adjugate) of A. For a 2x2 matrix [[a, b], [c, d]], the adjoint is [[d, -b], [-c, a]]. For our matrix, the adjoint is [[4, -3], [-1, 2]].
Step 4: Use the formula for the inverse of A, which is A^(-1) = (1/det(A)) * adj(A). We already found det(A) = 5 and adj(A) = [[4, -3], [-1, 2]].
Step 5: Substitute the values into the formula: A^(-1) = (1/5) * [[4, -3], [-1, 2]].
Step 6: Multiply each element of the adjoint by 1/5 to get the final inverse: A^(-1) = [[4/5, -3/5], [-1/5, 2/5]].

Matrix Inversion – Understanding how to calculate the inverse of a 2x2 matrix using the formula involving the determinant and adjoint.
Determinant Calculation – Calculating the determinant of a 2x2 matrix as a prerequisite for finding the inverse.
Adjoint of a Matrix – Finding the adjoint (or adjugate) of a matrix, which is necessary for computing the inverse.

If A = [[2, 3], [1, 4]], what is the inverse of A?

What’s inside this PDF?

If A = [[2, 3], [1, 4]], what is the inverse of A?

Practice Questions

Questions & Step-by-Step Solutions

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