2: HW3 Consider the planes {( ) [x+0₁+0₂=1} and {(²) | Ox+y+z=2} Ix- Ĉ Ñ= ? Find their normals. Solve the system Note that z to find the line where they intersect What is the direction of that line? Check it is I to both normals. a point (1) (32) · (6) = ? Now plug is free. Hint 1x +0y +Oz = 1 Ox+ly +12=2 (€)-(6) - ? = N= ? Ñ= Plug in 2=0 to find on the line. Check and (ž). (i) = ? in 2=1 to find another (2) on the line. Check: and (ž) - (i) = ? the answers should be I and 2 taks all the det producto requested bor/nA quick glance at our algorithm: Our Algorithm to Reduce Start with the top now and the first column on the left. L Is the leftmost colum YES all zeroes? NO Is the top left entry zero? NO Is the top left entry a one? YES YES Box the top left entry because it is leader YES NO Are the entries below this lander all zeroes? LUNA and HNE → an Augmented This column is done so cover it NO - Matrix to Echelon Form SWITCH the top row with the first row beneath it that has a zero left entry Are there any mes remaining on the left side of the maria? SCALE the top row so that the top left entry scales to one cover it This column is done so and the top row is done so cover it too YES SKEW each with montere entry below the leader by the leader's now to change the nonzero entry to zere Are there any rows remaining? YES INO The matrix is in Echelon Form NO

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