Question

(a) Determine a and b such that, \begin{bmatrix} 2 & 3 \\ 4 & 6 \end{bmatrix} \begin{bmatrix} a \\ b \end{bmatrix} = \begin{bmatrix} 13 & 23 \\ 26 & 46 \end{bmatrix} (b) Given the following system of equations. x - y + z = 1 2y - z = 4 2x + 3y = 7 Solve the system using (i) Inverse Matrix (ii) Cramer's rule

          (a) Determine a and b such that, \begin{bmatrix} 2 & 3 \\ 4 & 6 \end{bmatrix} \begin{bmatrix} a \\ b \end{bmatrix} = \begin{bmatrix} 13 & 23 \\ 26 & 46 \end{bmatrix} (b) Given the following system of equations. x - y + z = 1 2y - z = 4 2x + 3y = 7 Solve the system using (i) Inverse Matrix (ii) Cramer's rule

(a) Determine a and b such that,
< b m a t r i x >

< b m a t r i x >
=
< b m a t r i x >
(b) Given the following system of equations. x - y + z = 1 2y - z = 4 2x + 3y = 7 Solve the system using (i) Inverse Matrix (ii) Cramer's rule

Added by James D.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Madhur L

07/19/2023

Step 1

First, let's multiply the matrices on the left side: [[2,3],[4,6]] * [[a,7],[3,b]] = [[2a + 9, 21 + 3b],[4a + 18, 42 + 6b]] Now, set this equal to the matrix on the right side: [[2a + 9, 21 + 3b],[4a + 18, 42 + 6b]] = [[13,23],[26,46]] Show more…

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(a) Determine a and b such that, [[2,3],[4,6]][[a,7],[3,b]]=[[13,23],[26,46]] (b) Given the following system of equations: x - y + z = 1 2y - z = 4 2x + 3y = 7 Solve the system using: (i) Inverse Matrix (ii) Cramer's Rule