determinant - 2025 ACF Winter

Question

A coordinate-free definition of this operation relies on the top exterior power defining a one-dimensional space. (10[2])SL(n) (“S-L-N”) is the kernel of a homomorphism defined by this operation (10[1])from GL(n) (10[2])(“G-L-N”) to (10[1])the non-zero (10[3])reals (10[1])under multiplication. (10[3])Unusually, (10[1])this operation (10[1])is only introduced towards the end of a textbook by Sheldon (10[1])Axler (10[4])called (10[3])Linear (10[3])Algebra (10[1])Done (10[1])Right, (10[4]-5[1])which defines (10[1])this (10[1])operation as the unique (10[1])alternating (10[1])multilinear (10[1])form (10[1])up to (-5[2])scaling. (10[1])The output of this operation equals the constant (-5[1])term of the characteristic polynomial. (10[3]-5[2])The general linear (10[1])group excludes (10[1])matrices (10[1])which output (10[1])zero (-5[1])under (10[1])this operation (10[3])since (10[1])they are (-5[1])non-invertible. (10[8])For 10 (-5[1])points, (10[1]-5[2])name (10[2])this (10[1])operation that, (10[1])for a two-by-two matrix, equals (10[1])“a (10[1])d (10[5])minus (10[2]-5[1])b (10[2])c.” (0[1])■END■ (10[11]0[3])

ANSWER: determinant [or det]

<Editors, Other Science>

= Average correct buzz position

Summary


Northern California	Main	Y	4	100%	0%	25%	59.00
Southern California	Main	Y	6	100%	0%	17%	60.67
Florida	Main	Y	6	83%	0%	0%	89.60
Great Lakes	Main	Y	7	86%	0%	43%	94.00
Lower Mid-Atlantic	Main	Y	10	90%	0%	10%	88.56
Upper Mid-Atlantic (2)	Main	Y	5	100%	0%	20%	77.80
Lower Midwest	Main	Y	4	100%	0%	0%	101.00
Upper Midwest	Main	Y	10	90%	0%	20%	55.67
North	Main	Y	5	100%	0%	0%	80.60
Northeast	Main	Y	12	100%	0%	0%	67.83
Northwest	Main	Y	4	100%	0%	0%	56.50
South Central	Main	Y	8	100%	0%	13%	82.00
Southeast	Main	Y	8	100%	0%	25%	85.88
Upstate NY	Main	Y	1	100%	0%	0%	28.00

Buzzes

Player	Team	Opponent	Buzz Position	Value
Alex Akridge	Indiana A	Michigan C	15	10
Grant Koh	Michigan D	Notre Dame D	15	10
Abby Smith	Berkeley B	Berkeley E	26	10
Nathan Sheffield	MIT A	Harvard	28	10
Cade Reinberger	RIT B	Cornell-DII	28	10
Will Huang	Wisconsin	Nebraska	29	10
Luke Simon	Alberta B	McGill D	31	10
Matthew Sumanen	Georgia Tech A	Vanderbilt A	31	10
Will McCurley	Auburn A	Vanderbilt B	31	10
Michael Zheng	Amherst A	Brown A	32	10
Swapnil Garg	Berkeley C	Berkeley D	34	10
Kevin Ye	Simon Fraser	British Columbia D	34	10
Ezra Santos	Chicago A	Purdue A	34	10
Sidarth Erat	MIT B	Brandeis Clemenceau	35	10
Raymond Jiang	Illinois C	Michigan A	37	10
John McQueen	South Carolina B	Virginia B	48	10
Eli Zimmerman	Tufts A	Brandeis Lloyd George	49	10
Skand Parvatikar	Arizona State A	Northwestern A	49	10
Clio Selyuzhitsky	UCSD What Hath God Wrought	UCI	49	10
Tai Belke	British Columbia A	British Columbia B	49	10
Jeevan Iyadurai	UF E	UF B	50	10
George Matsumura	Washington B	Washington A	50	10
Dmitri Anh-Minh Tran	UCSB	UCLA D	50	10
Akshay Seetharam	Claremont Scripps	Claremont Pitzer	51	10
Kaiwen Xiao	UCLA B	UCSD Two Running Violet V Forms	51	10
Daniel Abrams	Rutgers C	Vassar A	51	10
Ryan Lee	Brown C	BU	52	10
Parker McCoig	Tennessee A	Virginia Tech A	53	10
Karthik Jayaram	UCLA A	USC	54	10
Jake Meltzer	CWRU A	OSU B	54	10
Aneesh Shrotriya	Purdue B	Louisville A	54	-5
Eames Weeks	Brown B	Tufts B	54	10
Elijah Pollock	UTD A	Arizona State B	54	10
Dennis Yang	Michigan B	Notre Dame C	56	10
Ben Hellman	Swarthmore A	Lehigh B	57	10
Alec Riso	Cornell-UG	Williams	61	10
Michał Gerasimiuk	Stanford A	Berkeley A	62	10
Zachary Joseph	Columbia A	Columbia C	63	10
Samuel Lipsutz	Chicago C	Illinois A	64	10
Stephen Walsh	Northwestern B	Texas A	66	-5
Danny Han	Stanford C	Stanford B	66	-5
Osbaldo Porrua	UIC	Chicago B	67	10
Ishan Joshi	Rutgers B	Lehigh A	75	-5
Andrew McKenzie	OSU D	OSU A	80	-5
Aditya Patnaik	OSU C	Pitt A	80	10
Graham Lucas	Bowdoin B	Amherst B	80	10
Caleb West	Kentucky	Illinois B	80	-5
Emerson Patmore	Georgia Tech C	Georgia Tech D	80	10
Jeremy Mau	Northwestern C	Iowa	83	10
Jim Fan	North Carolina A	Liberty A	85	10
Roy Yang	WashU B	Missouri B	86	10
Christopher Jenkins	UCF B	UF A	88	10
Anvit Watwani	UCLA C	UCSD Vices and Virtues	89	-5
Puna Ekka	Minnesota A	Carleton	90	10
Milo Scanlon	Macalester B	Macalester A	92	10
Wyatt Johnson	CWRU B	MSU A	92	10
Malachi Ledford	Tusculum	Tennessee B	92	10
Sriram Susarla	British Columbia C	Alberta	93	10
Abby Keith	Liberty B	James Madison	95	-5
Alex Feller	Minnesota C	Minnesota B	96	10
S. A. Shenoy	Georgia Tech B	Bruin A	96	10
John John Groger	WashU A	Missouri A	96	10
Ryan Gomes	Melbourne A	FSU	96	10
Brian Lai	Virginia A	North Carolina B	96	10
Ilyas Choukri	Virginia Tech B	North Carolina C	96	10
Jacob Chambers	Iowa State	St. Thomas	96	10
Peter Nelson	Yale B	Brandeis Orlando	96	10
Sawyer Smith	Mississippi State A	Auburn B	98	-5
Nathan Woolery	Louisville B	Indiana B	99	10
Jacob Evans	MSU B	Kenyon A	99	-5
Keith Delarosa	UAB A	Huntsville A	99	-5
Shiva Tegulla	UCF A	FIU	100	10
Jisoo Yoo	Texas B	UCO	100	10
Wesley Stine	Clemson A	South Carolina A	101	10
Niki Ilia	BC B	Bowdoin A	103	10
Alexandra Duan	Columbia B	Rowan A	108	10
Sumukh Murthy	UCSD Vices and Virtues	UCLA C	109	10
Jason Beardsley	Pitt C	Kenyon B	110	10
Thomas Thatcher	Truman State	WashU C	110	10
Chase Barrick	Lehigh A	Rutgers B	110	10
Spencer Thomas	Yale A	Dartmouth	110	10
Ethan Burks	Huntsville B	Alabama B	110	10
Vincent Chen	Pitt B	CWRU D	111	-5
Mason Evans	Tulsa	Rose State	111	10
Jackson McDonald	Alabama A	Sewanee A	111	10
Theodor Martin	WashU D	William Woods	112	10
Abbott Sherwin	NC State	Roanoke	112	10
Erin Williams	James Madison	Liberty B	113	0
Kathleen Perez	ERAU B	ERAU A	114	0
Yishak Kelkay	ERAU A	ERAU B	114	0
Aidan Bernardo	Melbourne B	USF	114	10
Roxanne Tang	OSU A	OSU D	114	10
Christopher Dech	Brandeis Wilson	BC A	114	10
Doug Frederick	Auburn B	Mississippi State A	114	10
Sri Lnu	Clemson B	Liberty C	114	10
Jiping Fang	Illinois B	Kentucky	114	10
Derek Kuldinow	Stanford B	Stanford C	114	10
Wren Davis	CWRU D	Pitt B	114	10
Beckett Gilmore	Louisville A	Purdue B	114	0
Matthew He	Texas A	Northwestern B	114	10
Young Fenimore Lee	Ohio	UTD B	114	10
Kad Daniels	Huntsville A	UAB A	114	10

Northern California

Main

100%

25%

59.00

Southern California

Main

100%

17%

60.67

Florida

Main

83%

89.60

Great Lakes

Main

86%

43%

94.00

Lower Mid-Atlantic

Main

90%

10%

88.56

Upper Mid-Atlantic (2)

Main

100%

20%

77.80

Lower Midwest

Main

100%

101.00

Upper Midwest

Main

90%

20%

55.67

North

Main

100%

80.60

Northeast

Main

100%

67.83

Northwest

Main

100%

56.50

South Central

Main

100%

13%

82.00

Southeast

Main

100%

25%

85.88

Upstate NY

Main

100%

28.00

Player

Team

Opponent

Buzz Position

Value

Alex Akridge

Indiana A

Michigan C

Grant Koh

Michigan D

Notre Dame D

Abby Smith

Berkeley B

Berkeley E

Nathan Sheffield

MIT A

Harvard

Cade Reinberger

RIT B

Cornell-DII

Will Huang

Wisconsin

Nebraska

Luke Simon

Alberta B

McGill D

Matthew Sumanen

Georgia Tech A

Vanderbilt A

Will McCurley

Auburn A

Vanderbilt B

Michael Zheng

Amherst A

Brown A

Swapnil Garg

Berkeley C

Berkeley D

Kevin Ye

Simon Fraser

British Columbia D

Ezra Santos

Chicago A

Purdue A

Sidarth Erat

MIT B

Brandeis Clemenceau

Raymond Jiang

Illinois C

Michigan A

John McQueen

South Carolina B

Virginia B

Eli Zimmerman

Tufts A

Brandeis Lloyd George

Skand Parvatikar

Arizona State A

Northwestern A

Clio Selyuzhitsky

UCSD What Hath God Wrought

UCI

Tai Belke

British Columbia A

British Columbia B

Jeevan Iyadurai

UF E

UF B

George Matsumura

Washington B

Washington A

Dmitri Anh-Minh Tran

UCSB

UCLA D

Akshay Seetharam

Claremont Scripps

Claremont Pitzer

Kaiwen Xiao

UCLA B

UCSD Two Running Violet V Forms

Daniel Abrams

Rutgers C

Vassar A

Ryan Lee

Brown C

Parker McCoig

Tennessee A

Virginia Tech A

Karthik Jayaram

UCLA A

USC

Jake Meltzer

CWRU A

OSU B

Aneesh Shrotriya

Purdue B

Louisville A

-5

Eames Weeks

Brown B

Tufts B

Elijah Pollock

UTD A

Arizona State B

Dennis Yang

Michigan B

Notre Dame C

Ben Hellman

Swarthmore A

Lehigh B

Alec Riso

Cornell-UG

Williams

Michał Gerasimiuk

Stanford A

Berkeley A

Zachary Joseph

Columbia A

Columbia C

Samuel Lipsutz

Chicago C

Illinois A

Stephen Walsh

Northwestern B

Texas A

-5

Danny Han

Stanford C

Stanford B

-5

Osbaldo Porrua

UIC

Chicago B

Ishan Joshi

Rutgers B

Lehigh A

-5

Andrew McKenzie

OSU D

OSU A

-5

Aditya Patnaik

OSU C

Pitt A

Graham Lucas

Bowdoin B

Amherst B

Caleb West

Kentucky

Illinois B

-5

Emerson Patmore

Georgia Tech C

Georgia Tech D

Jeremy Mau

Northwestern C

Iowa

Jim Fan

North Carolina A

Liberty A

Roy Yang

WashU B

Missouri B

Christopher Jenkins

UCF B

UF A

Anvit Watwani

UCLA C

UCSD Vices and Virtues

-5

Puna Ekka

Minnesota A

Carleton

Milo Scanlon

Macalester B

Macalester A

Wyatt Johnson

CWRU B

MSU A

Malachi Ledford

Tusculum

Tennessee B

Sriram Susarla

British Columbia C

Alberta

Abby Keith

Liberty B

James Madison

-5

Alex Feller

Minnesota C

Minnesota B

S. A. Shenoy

Georgia Tech B

Bruin A

John John Groger

WashU A

Missouri A

Ryan Gomes

Melbourne A

FSU

Brian Lai

Virginia A

North Carolina B

Ilyas Choukri

Virginia Tech B

North Carolina C

Jacob Chambers

Iowa State

St. Thomas

Peter Nelson

Yale B

Brandeis Orlando

Sawyer Smith

Mississippi State A

Auburn B

-5

Nathan Woolery

Louisville B

Indiana B

Jacob Evans

MSU B

Kenyon A

-5

Keith Delarosa

UAB A

Huntsville A

-5

Shiva Tegulla

UCF A

FIU

100

Jisoo Yoo

Texas B

UCO

100

Wesley Stine

Clemson A

South Carolina A

101

Niki Ilia

BC B

Bowdoin A

103

Alexandra Duan

Columbia B

Rowan A

108

Sumukh Murthy

UCSD Vices and Virtues

UCLA C

109

Jason Beardsley

Pitt C

Kenyon B

110

Thomas Thatcher

Truman State

WashU C

110

Chase Barrick

Lehigh A

Rutgers B

110

Spencer Thomas

Yale A

Dartmouth

110

Ethan Burks

Huntsville B

Alabama B

110

Vincent Chen

Pitt B

CWRU D

111

-5

Mason Evans

Tulsa

Rose State

111

Jackson McDonald

Alabama A

Sewanee A

111

Theodor Martin

WashU D

William Woods

112

Abbott Sherwin

NC State

Roanoke

112

Erin Williams

James Madison

Liberty B

113

Kathleen Perez

ERAU B

ERAU A

114

Yishak Kelkay

ERAU A

ERAU B

114

Aidan Bernardo

Melbourne B

USF

114

Roxanne Tang

OSU A

OSU D

114

Christopher Dech

Brandeis Wilson

BC A

114

Doug Frederick

Auburn B

Mississippi State A

114

Sri Lnu

Clemson B

Liberty C

114

Jiping Fang

Illinois B

Kentucky

114

Derek Kuldinow

Stanford B

Stanford C

114

Wren Davis

CWRU D

Pitt B

114

Beckett Gilmore

Louisville A

Purdue B

114

Matthew He

Texas A

Northwestern B

114

Young Fenimore Lee

Ohio

UTD B

114

Kad Daniels

Huntsville A

UAB A

114