Question

12-3 Find the inverse of the matrix $A = \begin{bmatrix} 1 & 1 & 1 \ 1 & 2 & 3 \ 1 & 4 & 9 \end{bmatrix}$ by using the formula $A^{-1} = \frac{1}{det \ A} Adj \ A$ (see Section 12.2). 12-4 Let A be an invertible matrix. Show that $det(A^{-1}) = 1/(det A)$. HINT: Apply det to both sides of the equation $AA^{-1} = I.$

          12-3 Find the inverse of the matrix
$A = \begin{bmatrix} 1 & 1 & 1 \ 1 & 2 & 3 \ 1 & 4 & 9 \end{bmatrix}$
by using the formula $A^{-1} = \frac{1}{det \ A} Adj \ A$ (see Section 12.2).
12-4 Let A be an invertible matrix. Show that $det(A^{-1}) = 1/(det A)$.
HINT: Apply det to both sides of the equation $AA^{-1} = I.$

12-3 Find the inverse of the matrix
A =
< b m a t r i x >
by using the formula A^-1 = (1)/(det A) Adj A (see Section 12.2).
12-4 Let A be an invertible matrix. Show that det(A^-1) = 1/(det A).
HINT: Apply det to both sides of the equation AA^-1 = I.

Added by Samuel S.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Naresh Bagrecha

Step 1

We will find A^{-1} using A^{-1} = (1/det A) Adj A. Show more…

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12-3 Find the inverse of the matrix A=[[1,1,1],[1,2,3],[1,4,9]] by using the formula A^(-1)=(1)/(detA)AdjA (see Section 12.2). 12-4 Let A be an invertible matrix. Show that det(A^(-1))=(1)/(detA). HinT: Apply det to both sides of the equation AA^(-1)=I. 12-3Find the inverse of the matrix A= by using the formula A - Adj A (see Section 12.2). det A 12-4 Let A be an invertible matrix. Show that det(A-1) = 1/(det A) HINT: Apply det to both sides of the equation AA-1 = I.